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Worksheets

قواعد الاشتقاق

Total questions: 12

Worksheet time: 6mins

Name
Class
Date
1.

 y=x4y=x^4  مشتقة الدالة 

a)

4x

b)

 4x34x^3  

c)

 4x54x^5  

d)

 x3x^3  

2.

 f(x)=1xf\left(x\right)=\frac{\text{1}}{\text{x}}  ,  ..  

a)

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

b)

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

c)

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

d)

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

3.

 f(x)=xf\left(x\right)=\sqrt{x}  

a)

 f(x)=2xf'\left(x\right)=2\sqrt{x}  

b)

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

c)

 f(x)=12xf'\left(x\right)=\frac{1}{2\sqrt{x}}  

d)

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

4.

 f(x)=x2020f\left(x\right)=x^{2020}  

a)

 f(x)=2019x2020f'\left(x\right)=2019x^{2020}  

b)

 f(x)=2020x2019f'\left(x\right)=2020x^{2019}  

c)

 f(x)=2020f'\left(x\right)=2020  

d)

 f(x)=2019f'\left(x\right)=2019  

5.

 f(x)=x56f\left(x\right)=x^{\frac{5}{6}}  

a)

 f(x)=56x16f'\left(x\right)=\frac{5}{6}x^{\frac{1}{6}}  

b)

 f(x)=65x16f'\left(x\right)=\frac{6}{5}x^{\frac{1}{6}}  

c)

 f(x)=56x16f'\left(x\right)=\frac{5}{6x^{\frac{1}{6}}}  

d)

 f(x)=65x16f'\left(x\right)=\frac{6}{5x^{\frac{1}{6}}}  

6.

 f(x)=3x7f\left(x\right)=3x^{-7}  

a)

 f(x)=21x6f\left(x\right)=-\frac{21}{x^6}  

b)

 f(x)=21x8f\left(x\right)=-\frac{21}{x^8}  

c)

 f(x)=21x6f\left(x\right)=\frac{21}{x^6}  

d)

 f(x)=21x8f\left(x\right)=\frac{21}{x^8}  

7.


 f(x)=3f\left(x\right)=\sqrt{3}  أوجد مشتقة الدالة

a)

ϕ\phi

b)

10

c)

0

d)

10x

8.

أوجد مشتقة الضرب للدالة :
 f(x)=(2χ25)(x+3)f\left(x\right)=\left(2\chi^2-5\right)\left(x+3\right)  

a)

 6x2+76x^2+7  

b)

 6x2+12x56x^2+12x-5  

c)

 77  

d)

 6x76x-7  

9.

جد مشتقة الدالة
 f(X) = 5x2 +23x +1f\left(X\right)\ =\ \frac{5x^2\ +2}{3x\ +1}  

a)

 (3x+1)(10x)(5x2+2)(3)(3x+1)2\frac{\left(3x+1\right)\left(10x\right)-\left(5x^2+2\right)\left(3\right)}{\left(3x+1\right)^2}  

b)

 (3x+1)(5x) (5x +2)(3x+1)2\frac{\left(3x+1\right)\left(5x\right)-\ \left(5x\ +2\right)}{\left(3x+1\right)^2}  

c)

 (5x+1)2(2) 6x(2)(5x+2)2\frac{\left(5x+1\right)^2\left(2\right)-\ 6x\left(2\right)}{\left(5x+2\right)^2}  

d)

 (5x+2)(3x+1)2\frac{\left(5x+2\right)}{\left(3x+1\right)^2}  

10.

جد مشتقة

a)

 (8x +2  12x2)(5x2 + 1)\left(8x\ +2\ -\ 12x^2\right)\left(5x^2\ +\ -1\right)  

b)


 (8x2+3)(x3+x +x2)\left(8x^2+3\right)\left(x^3+x\ +x^2\right)  

c)

 (x2+x3+x)(16x)+(8x2+3)(2x +3x2 +1)\left(x^2+x^3+x\right)\left(16x\right)+\left(8x^2+3\right)\left(2x\ +3x^2\ +1\right)  

d)

 (5x  1)2x\frac{\left(5x\ -\ 1\right)}{2x}  

11.
a)
b)
c)
d)
12.
a)

-2

b)

0

c)

1

d)

2