wayground logo

Free Printable Worksheets

Font size

S
M
L
XL
Worksheets

derivate somma prodotto fratte

Total questions: 29

Worksheet time: 29mins

Name
Class
Date
1.

 f(x)=2senx⋅cos⁡x, df(x)=?f\left(x\right)=2senx\cdot\cos x,\ df\left(x\right)=?  

a)

 f′(x)=2cos⁡x⋅senxf'\left(x\right)=2\cos x\cdot senx  

b)

 f′(x)=2(sen2x+cos⁡2x)f'\left(x\right)=2\left(sen^2x+\cos^2x\right)  

c)

 f′(x)=2(cos⁡2x−sen2x)f'\left(x\right)=2\left(\cos^2x-sen^2x\right)  

d)

 f′(x)=2cos⁡(cos⁡x)senxf'\left(x\right)=2\cos\left(\cos x\right)senx  

2.

 f(x)=tgx=senxcos⁡x, Df(x)=?f\left(x\right)=tgx=\frac{senx}{\cos x},\ Df\left(x\right)=?  

a)

 f′(x)=1cos⁡2xf'\left(x\right)=\frac{1}{\cos^2x}  

b)

 f′(x)=senxcos⁡2xf'\left(x\right)=\frac{senx}{\cos^2x}  

c)

 f′(x)=cos⁡x−senxsen2xf'\left(x\right)=\frac{\cos x-senx}{sen^2x}  

d)

 f′(x)=senx+cos⁡xcos⁡2xf'\left(x\right)=\frac{senx+\cos x}{\cos^2x}  

3.

 f(x)=xx2+1, Df(x)=?f\left(x\right)=\frac{x}{x^2+1},\ Df\left(x\right)=?  

a)

 f′(x)=(3x2+1)(x2+1)f'\left(x\right)=\frac{\left(3x^2+1\right)}{\left(x^2+1\right)}  

b)

 f′(x)=(2x2−1)(x2+1)2f'\left(x\right)=\frac{\left(2x^2-1\right)}{\left(x^2+1\right)^2}  

c)

 f′(x)=(1−x2)(x2+1)2f'\left(x\right)=\frac{\left(1-x^2\right)}{\left(x^2+1\right)^2}  

d)

 f′(x)=(x2−1)(x2+1)2f'\left(x\right)=\frac{\left(x^2-1\right)}{\left(x^2+1\right)^2}  

4.

 f(x)=xex, Df(x)=?f\left(x\right)=\frac{x}{e^x},\ Df\left(x\right)=?  

a)

 f′(x)=1e2xf'\left(x\right)=\frac{1}{e^{2x}}  

b)

 f′(x)=(1−x)exf'\left(x\right)=\frac{\left(1-x\right)}{e^x}  

c)

 f′(x)=(ex+x)e2xf'\left(x\right)=\frac{\left(e^x+x\right)}{e^{2x}}  

d)

 f′(x)=(ex−x)exf'\left(x\right)=\frac{\left(e^x-x\right)}{e^x}  

5.

 f(x)=xex+2x3+1, Df(x)=?f\left(x\right)=xe^x+2x^3+1,\ Df\left(x\right)=?  

a)

 f′(x)=ex+6x2f'\left(x\right)=e^x+6x^2  

b)

 f′(x)=ex+xex+6x2f'\left(x\right)=e^x+xe^x+6x^2  

c)

 f′(x)=ex+x+6x2f'\left(x\right)=e^x+x+6x^2  

d)

 f′(x)=xex+6x2f'\left(x\right)=xe^x+6x^2  

6.

 f(x)=x2⋅ln⁡x, Df(x)=? f\left(x\right)=x^2\cdot\ln x,\ Df\left(x\right)=?\   

a)

 f′(x)=2x⋅ln⁡xf'\left(x\right)=2x\cdot\ln x  

b)

 f′(x)=2x⋅ln⁡x+x2f'\left(x\right)=2x\cdot\ln x+x^2  

c)

 f′(x)=2x⋅ln⁡x+xf'\left(x\right)=2x\cdot\ln x+x  

d)

 f′(x)=2x⋅ln⁡x+ln⁡xf'\left(x\right)=2x\cdot\ln x+\ln x  

7.

 f(x)=x+1x−2, Df(x)=?f\left(x\right)=\frac{x+1}{x-2},\ Df\left(x\right)=?  

a)

 f′(x)=1(x−2)2f'\left(x\right)=\frac{1}{\left(x-2\right)^2}  

b)

 f′(x)=−3(x−2)2f'\left(x\right)=\frac{-3}{\left(x-2\right)^2}  

c)

 f′(x)=−2x(x−2)2f'\left(x\right)=\frac{-2x}{\left(x-2\right)^2}  

d)

 f′(x)=3x−1(x−2)2f'\left(x\right)=\frac{3x-1}{\left(x-2\right)^2}  

8.

 f(x)=x2x−1, Df(x)=?f\left(x\right)=\frac{x^2}{x-1},\ Df\left(x\right)=?  

a)

 f′(x)=x2(x−1)2f'\left(x\right)=\frac{x^2}{\left(x-1\right)^2}  

b)

 f′(x)=(x2−2x)(x−1)2f'\left(x\right)=\frac{\left(x^2-2x\right)}{\left(x-1\right)^2}  

c)

 f′(x)=x2−2x+1(x−2)2f'\left(x\right)=\frac{x^2-2x+1}{\left(x-2\right)^2}  

d)

 f′(x)=x2−1(x−2)2f'\left(x\right)=\frac{x^2-1}{\left(x-2\right)^2}  

9.
La funzione y=1+ln(x) è la derivata di una sola delle seguenti funzioni. Quale?
a)
y=x+1/x
b)
y=x+ln(x)
c)
y=x-ln(x)
d)
y=x⋅ln(x)
10.
La derivata di y=ex⋅cos(x) è:
a)
y'=ex⋅(cos(x)+sin(x))
b)
y'=ex⋅(cos(x)-sin(x))
c)
y'=ex⋅(cos(2x))
d)
y'=cos(x)⋅(ex-sin(x))
11.

 f(x)=ex−x3+3f\left(x\right)=e^x-x^3+3  

a)

 f′(x)=ex+3f'\left(x\right)=e^x+3  

b)

 f′(x)=ex−3x2f'\left(x\right)=e^x-3x^2  

c)

 f′(x)=ex−x2+3f'\left(x\right)=e^x-x^2+3  

d)

 f′(x)=x−3f'\left(x\right)=x-3  

12.

 f(x)=x+ln⁡xf\left(x\right)=x+\ln x  

a)

 f′(x)=1+1xf'\left(x\right)=1+\frac{\text{1}}{\text{x}}  

b)

 f′(x)=x+1f'\left(x\right)=x+1  

c)

 f′(x)=x+1xf'\left(x\right)=\frac{x+1}{x}  

d)

 f′(x)=x−1xf'\left(x\right)=x-\frac{1}{x}  

13.

 f(x)=x3+x2−x+1f\left(x\right)=x^3+x^2-x+1  

a)

 f′(x)=3x2+2x−1f'\left(x\right)=3x^2+2x-1  

b)

 f′(x)=3x+2f'\left(x\right)=3x+2  

c)

 f′(x)=3x+1f'\left(x\right)=3x+1  

d)

 f′(x)=3x2+1f'\left(x\right)=3x^2+1  

14.

 f(x)=(x−2)exf\left(x\right)=\left(x-2\right)e^x  

a)

 f′(x)=(x−1)exf'\left(x\right)=\left(x-1\right)e^x  

b)

 f′(x)=(x−2)exf'\left(x\right)=\left(x-2\right)e^x  

c)

 f′(x)=exf'\left(x\right)=e^x  

d)

 f′(x)=1+exf'\left(x\right)=1+e^x  

15.

 f(x)=x−1xf\left(x\right)=x-\frac{1}{x}  

a)

 f′(x)=1+1x2f'\left(x\right)=1+\frac{1}{x^2}  

b)

 f′(x)=1−1x2f'\left(x\right)=1-\frac{1}{x^2}  

c)

 f′(x)=x2+1x2f'\left(x\right)=\frac{x^2+1}{x^2}  

d)

 f′(x)=1−ln⁡xf'\left(x\right)=1-\ln x  

16.

 f(x)=sin⁡x+cos⁡xf\left(x\right)=\sin x+\cos x  

a)

 f′(x)=cos⁡x−sin⁡xf'\left(x\right)=\cos x-\sin x  

b)

 f′(x)=cos⁡x+sin⁡xf'\left(x\right)=\cos x+\sin x  

c)

 f′(x)=−cos⁡x+sin⁡xf'\left(x\right)=-\cos x+\sin x  

d)

 f′(x)=−cos⁡x−sin⁡xf'\left(x\right)=-\cos x-\sin x  

17.

 f(x)=sin⁡x+cos⁡x     →     f′(x)=f\left(x\right)=\sin x+\cos x\ \ \ \ \ \rightarrow\ \ \ \ \ f'\left(x\right)=  



(a)  

18.

 f(x)=2x2, Df(x)=?f\left(x\right)=\frac{2}{x^2},\ Df\left(x\right)=?  

a)

 f′(x)=2x2f'\left(x\right)=2x^2  

b)

 f′(x)=2xf'\left(x\right)=\frac{2}{x}  

c)

 f′(x)=2x3f'\left(x\right)=\frac{2}{x^3}  

d)

 f′(x)=−4x3f'\left(x\right)=-\frac{4}{x^3}  

19.

 f(x)=x+1x2, Df(x)=?f\left(x\right)=\sqrt{x}+\frac{1}{x^2},\ Df\left(x\right)=?  

a)

 f′(x)=12x−1x3f'\left(x\right)=\frac{1}{2\sqrt{x}}-\frac{1}{x^3}  

b)

 f′(x)=12x−2x3f'\left(x\right)=\frac{1}{2\sqrt{x}}-\frac{2}{x^3}  

c)

 f′(x)=1x−1x3f'\left(x\right)=\frac{1}{\sqrt{x}}-\frac{1}{x^3}  

d)

 f′(x)=2x−1x3f'\left(x\right)=2\sqrt{x}-\frac{1}{x^3}  

20.

 f(x)=x−2sin⁡x     →     f′(x)=f\left(x\right)=x-2\sin x\ \ \ \ \ \rightarrow\ \ \ \ \ f'\left(x\right)=  



(a)  

21.

 f(x)=3ln⁡x+2cos⁡x+x2f\left(x\right)=3\ln x+2\cos x+x^2  

a)

 f′(x)=3x−2senx+2xf'\left(x\right)=\frac{3}{x}-2senx+2x  

b)

 f′(x)=1x+2senx+2f'\left(x\right)=\frac{1}{x}+2senx+2  

c)

 f′(x)=3x+2senx+2xf'\left(x\right)=\frac{3}{x}+2senx+2x  

d)

 f′(x)=3x−2cos⁡x+2xf'\left(x\right)=\frac{3}{x}-2\cos x+2x  

22.

La derivata di

 f(x)=x⋅ln⁡xf\left(x\right)=x\cdot\ln x  è

a)

 1ln⁡x\frac{1}{\ln x}  

b)

 ln⁡x+1\ln x+1  

c)

1

d)

 1+1x1+\frac{1}{x}  

23.

 f(x)=x2⋅ln⁡xf\left(x\right)=x^2\cdot\ln x  

a)

 f′(x)=2x⋅ln⁡xf'\left(x\right)=2x\cdot\ln x  

b)

 f′(x)=2x⋅ln⁡x+x2f'\left(x\right)=2x\cdot\ln x+x^2  

c)

 f′(x)=2x⋅ln⁡x+xf'\left(x\right)=2x\cdot\ln x+x  

d)

 f′(x)=2x⋅ln⁡x+ln⁡xf'\left(x\right)=2x\cdot\ln x+\ln x  

24.

 f(x)=(x−2)exf\left(x\right)=\left(x-2\right)e^x  

a)

 f′(x)=(x−1)exf'\left(x\right)=\left(x-1\right)e^x  

b)

 f′(x)=(x−2)exf'\left(x\right)=\left(x-2\right)e^x  

c)

 f′(x)=exf'\left(x\right)=e^x  

d)

 f′(x)=1+exf'\left(x\right)=1+e^x  

25.

 f(x)=xx2+1f\left(x\right)=\frac{x}{x^2+1}  

a)

 f′(x)=(3x2+1)(x2+1)f'\left(x\right)=\frac{\left(3x^2+1\right)}{\left(x^2+1\right)}  

b)

 f′(x)=(2x2−1)(x2+1)2f'\left(x\right)=\frac{\left(2x^2-1\right)}{\left(x^2+1\right)^2}  

c)

 f′(x)=(1−x2)(x2+1)2f'\left(x\right)=\frac{\left(1-x^2\right)}{\left(x^2+1\right)^2}  

d)

 f′(x)=(x2−1)(x2+1)2f'\left(x\right)=\frac{\left(x^2-1\right)}{\left(x^2+1\right)^2}  

26.

 f(x)=xexf\left(x\right)=\frac{x}{e^x}  

a)

 f′(x)=1e2xf'\left(x\right)=\frac{1}{e^{2x}}  

b)

 f′(x)=(1−x)exf'\left(x\right)=\frac{\left(1-x\right)}{e^x}  

c)

 f′(x)=(ex+x)e2xf'\left(x\right)=\frac{\left(e^x+x\right)}{e^{2x}}  

d)

 f′(x)=(ex−x)exf'\left(x\right)=\frac{\left(e^x-x\right)}{e^x}  

27.

 f(x)=x+1x−2f\left(x\right)=\frac{x+1}{x-2}  

a)

 f′(x)=1(x−2)2f'\left(x\right)=\frac{1}{\left(x-2\right)^2}  

b)

 f′(x)=−3(x−2)2f'\left(x\right)=\frac{-3}{\left(x-2\right)^2}  

c)

 f′(x)=−2x(x−2)2f'\left(x\right)=\frac{-2x}{\left(x-2\right)^2}  

d)

 f′(x)=3x−1(x−2)2f'\left(x\right)=\frac{3x-1}{\left(x-2\right)^2}  

28.

f(x)=ln⁡x−2xf\left(x\right)=\frac{\ln x-2}{x}  

a)

f′(x)=3−ln⁡xx2f'\left(x\right)=\frac{3-\ln x}{x^2}  

b)

f′(x)=3+ln⁡x2x2f'\left(x\right)=\frac{3+\ln x^2}{x^2}  

c)

f′(x)=3ln⁡xx2f'\left(x\right)=\frac{3\ln x}{x^2}  

d)

f′(x)=ln⁡x−3xf'\left(x\right)=\frac{\ln x-3}{x^{ }}  

29.

 f(x)=tgx=senxcos⁡xf\left(x\right)=tgx=\frac{senx}{\cos x}  

a)

 f′(x)=1cos⁡2xf'\left(x\right)=\frac{1}{\cos^2x}  

b)

 f′(x)=senxcos⁡2xf'\left(x\right)=\frac{senx}{\cos^2x}  

c)

 f′(x)=cos⁡x−senxsen2xf'\left(x\right)=\frac{\cos x-senx}{sen^2x}  

d)

 f′(x)=senx+cos⁡xcos⁡2xf'\left(x\right)=\frac{senx+\cos x}{\cos^2x}  

Similar Resources on Wayground

ECUACIONES

24 questions

ECUACIONES

quiz

Worksheet

•

11th Grade

ÔN TẬP CUỐI HỌC KÌ 1

25 questions

ÔN TẬP CUỐI HỌC KÌ 1

quiz

Worksheet

•

12th Grade

pitágoras

24 questions

pitágoras

quiz

Worksheet

•

11th Grade

ulangkaji matemati ppt t4

25 questions

ulangkaji matemati ppt t4

quiz

Worksheet

•

12th Grade

Muestreo de Operaciones Básicas

25 questions

Muestreo de Operaciones Básicas

quiz

Worksheet

•

9th - 12th Grade

MT6 Wang

25 questions

MT6 Wang

quiz

Worksheet

•

12th Grade

Points, Lines, Planes

26 questions

Points, Lines, Planes

quiz

Worksheet

•

8th - 11th Grade

11th Q3 quiz2 Logarithms

24 questions

11th Q3 quiz2 Logarithms

quiz

Worksheet

•

11th Grade