Quiz about Derivadas exponenciales y logarítmicas

Question 1

Derivar

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

Accepted Answer

$$f´\left(x\right)=Cot\ x$$

Answer

$$f´\left(x\right)=\frac{1}{sen\ x}$$

Answer

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

Answer

$$f´\left(x\right)=Tan\ x$$

Question 2

$$f\left(x\right)=e^{\left(x^2+2x-15\right)}$$

Accepted Answer

f(x) = e^{(x+5)(x-3)}

Answer

f(x) = e^{(x+3)(x-5)}

Answer

f(x) = e^{(x-5)(x+3)}

Answer

f(x) = e^{(x-3)(x+5)}

Question 3

Calculate the derivative of the function:

$$f\left(x\right)=\ln\left(3x^2+4x+1\right)$$

Accepted Answer

$$f´\left(x\right)=\frac{6x+4}{3x^2+4x+1}$$

Answer

$$f´\left(x\right)=\frac{6x+4}{3x+4}$$

Answer

$$f´\left(x\right)=\frac{6x+4}{3x^2+4}$$

Answer

$$f´\left(x\right)=\frac{6x+4}{3x+1}$$

Question 4

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

Accepted Answer

$$f$$

Question 5

$$f\left(x\right)=3^{\cos x}$$

Accepted Answer

$$f$$

Question 6

$$f\left(x\right)=e^{x^4}$$

Accepted Answer

$$f$$

Question 7

$$f\left(x\right)=5^{\ln x}$$

Accepted Answer

$$f$$

Question 8

$$f\left(x\right)=6^{\cos x}$$

Accepted Answer

$$f$$

Question 9

$$y=\ln\left(5x+1\right)$$

Accepted Answer

$$\frac{ ext{d}x}{ ext{d}y}=\frac{5}{5x+1}$$

Answer

$$\frac{ ext{d}x}{ ext{d}y}=\frac{5}{\left(5x+1 ight)^2}$$

Question 10

$$f\left(x\right)=e^{\frac{1}{senx}}$$

Accepted Answer

$$f$$

Question 11

$$y=\ln\left(3x+8\right)^2$$

Accepted Answer

$$f$$

Question 12

$$y=\ln\left(\sqrt[2]{3-x^2}\right)$$

Accepted Answer

$$\frac{ ext{d}x}{ ext{d}y}=-\frac{x}{3-x^2}$$

Answer

$$\frac{ ext{d}x}{ ext{d}y}=\frac{x}{3-x^2}$$

Answer

$$\frac{ ext{d}x}{ ext{d}y}=-\frac{x}{3+x^2}$$

Answer

$$\frac{ ext{d}x}{ ext{d}y}=\frac{x^2}{3+x}$$

Question 13

$$y=\log\left(2x-1\right)$$

Accepted Answer

$$\frac{ ext{d}x}{ ext{d}y}=\frac{2\log e}{2x-1}$$

Answer

$$\frac{ ext{d}x}{ ext{d}y}=\frac{2\log e}{2x+1}$$

Question 14

$$f\left(x\right)=4^{\left(x^2-3x+2\right)}$$

Accepted Answer

f(x) = 4^{(x-1)(x-2)}

Answer

f(x) = 4^{(x+1)(x-2)}

Answer

f(x) = 4^{(x-1)(x+2)}

Answer

f(x) = 4^{(x+1)(x+2)}

Question 15

$$f\left(x\right)=3^{\left(\frac{x}{x^2+3}\right)}$$

Accepted Answer

$$f$$

Question 16

$$f\left(x\right)=7^{\cos x}$$

Accepted Answer

$$f$$

Question 17

$$g\left(t\right)=1+\left(2+t\right)e^{-t}$$

Accepted Answer

$$g$$

Question 18

$$g\left(x\right)=\frac{1}{\sqrt[2]{2}\pi}e^{-\frac{\left(x-3\right)^2}{2}}$$

Accepted Answer

$$g$$

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