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CADENA, EXPONENCIAL, LOG, TRIGONOMÉTRICAS

Total questions: 10

Worksheet time: 9mins

Name
Class
Date
1.

La derivada de f(x)=2x+3f\left(x\right)=\sqrt{2x+3} es 

a)

12x+3\frac{1}{\sqrt{2x+3}}  

b)

122x+3\frac{1}{2\sqrt{2x+3}}  

c)

22x+3\frac{2}{\sqrt{2x+3}}  

2.

Si la función f(x)=(x2−x+2)4f\left(x\right)=\left(x^2-x+2\right)^4 , hallar f´(0) 

a)

64

b)

-32

c)

20

d)

-16

3.

La derivada de la función

4sen2(3x−1)+3cos⁡(2x+1) es:4sen^2\left(3x-1\right)+3\cos\left(2x+1\right)\ es:  

a)

12sen(3x-1)cos(3x-1)

b)

-8sen(3x-1)cos(3x-1)

c)

12sen(3x-1)

d)

24cos(3x-1)

4.

La derivada de sen(4x+5)

a)

4 cos(x)

b)

cos(4x+5)

c)

-cos(4x+5)

d)

4cos(4x+5)

5.

Derivar

f(x)=2ex5f\left(x\right)=2e^{x^5}  

a)

f´(x)=2x4 ex5f´\left(x\right)=2x^{4\ }e^{x^5}  

b)

f´(x)=5x4 ex5f´\left(x\right)=5x^{4\ }e^{x^5}  

c)

f´(x)=10x4 ex5f´\left(x\right)=10x^{4\ }e^{x^5}  

d)

f´(x)=ex5f´\left(x\right)=e^{x^5}  

6.

Derivar

f(x)=8x2+1f\left(x\right)=8^{x^2+1}  

a)

f´(x)=2 In8f´\left(x\right)=2\ In8  

b)

f´(x)=2x In8f´\left(x\right)=2x\ In8  

c)

f´(x)=16xx2+1 ⋅In 16f´\left(x\right)=16x^{x^2+1}\ \cdot In\ 16  

d)

f´(x)=8x2+1 ⋅ In 8 ⋅2xf´\left(x\right)=8^{x^2+1}\ \cdot\ In\ 8\ \cdot2x  

7.

Deriva y simplifica: y=ln⁡(x+1x−1)y=\ln\left(\frac{x+1}{x-1}\right)  

a)

y=−2x(x−1)2y=\frac{-2x}{\left(x-1\right)^2}  

b)

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

c)

y=−2x2−1y=\frac{-2}{x^2-1}  

d)

y=−1x+1y=\frac{-1}{x+1}  

8.

Derivar

f(x)=Ln (sen x)f\left(x\right)=Ln\ \left(sen\ x\right)  

a)

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

b)

f´(x)=1cos⁡ xf´\left(x\right)=\frac{1}{\cos\ x}  

c)

f´(x)=Cot xf´\left(x\right)=Cot\ x  

d)

f´(x)=Tan xf´\left(x\right)=Tan\ x  

9.

Derivar

f(x)=log⁡5 (x2)f\left(x\right)=\log_5\ \left(x^2\right)  

a)

f´(x)=2x Ln 5f´\left(x\right)=\frac{2}{x\ Ln\ 5}  

b)

f´(x)=2x5x 2 Ln 2f´\left(x\right)=\frac{2x}{5x\ ^2\ Ln\ 2}  

c)

f´(x)=x2 Ln 5f´\left(x\right)=\frac{x}{2\ Ln\ 5}  

d)

f´(x)=1x Ln 5f´\left(x\right)=\frac{1}{x\ Ln\ 5}  

10.

Hallar la derivada de f(x)=(3x2−5x)3f\left(x\right)=\left(3x^2-5x\right)^3

a)

(18x−15)2(3x2−5x)2(18x−15)^2(3x^2−5x)^2  

b)

(18x−15)(3x2−5x)2\left(18x-15\right)\left(3x^2-5x\right)^2  

c)

(18x−15)(3x2−5x)3(18x−15)(3x^2−5x)^3  

d)

(18x−15)(3x−5)2(18x−15)(3x−5)^2