Question 1

The derivative of$ cos(5x)$

Accepted Answer

$-5sin(5x)$

Answer

$-5sin(x)$

Answer

$5sin(5x)$

Answer

$5cos(5x)$

Question 2

The derivative of tan($x^2$)

Accepted Answer

2x$sec^2$($x^2$)

Answer

2xtan($x^2$)

Answer

$2tan(x) $

Answer

2xsec($x^2$)

Question 3

What is the derivative of $sin^2$(2x)

Accepted Answer

$4sin(2x)cos(2x)$

Answer

$4sin(x)cos(x)$

Answer

$2sin(2x)cos(2x)$

Answer

$4sin(2x)$

Question 4

The derivative of$ sin(2x)cos(3x)$ is :

Accepted Answer

$2cos(2x)cos(3x) - 3sin(2x)sin(3x)$

Answer

$ -6cos(2x)sin(3x)$

Answer

$2cos(2x)cos(3x) + 3sin(2x)sin(3x)$

Answer

$ 6cos(2x)sin(3x)$

Question 5

If $y$= $e^\frac{1}{x}$  then   $\frac{dy}{dx}$ =

Accepted Answer

$\frac{-1}{x^2}e^\frac{1}{x}$

Answer

$\frac{1}{x^2}e^\frac{1}{x}$

Answer

$\frac{1}{x}e^{\frac{1}{x}-1}$

Answer

$e^\frac{1}{x}$

Question 6

If$ y$= ln(${x^2 + 3x +5}$ ) then $\frac{dy}{dx} =$

Accepted Answer

$\frac{2x+3}{x^2+3x+5}$

Answer

$(2x+3)$ ln(${x^2 + 3x +5}$ )

Answer

$\frac{2x+3}{ln(x^2+3x+5)}$

Answer

$\frac{1}{x^2+3x+5}$

Question 7

If $y= \frac{e^{2x}}{ln(3x)}$   then   $\frac{dy}{dx} = $

Accepted Answer

$\frac{2e^{2x}ln(3x)-\frac{e^{2x}}{x}}{ln^2(3x)}$

Answer

$\frac{2e^{2x}ln(3x)-\frac{e^{2x}}{x}}{ln(3x)}$

Answer

$\frac{2e^{2x}ln(3x)-\frac{e^{2x}}{3x}}{ln^2(3x)}$

Answer

$\frac{2e^{2x}ln(3x)+\frac{e^{2x}}{x}}{ln^2(3x)}$

Question 8

If $y = e^{(2x)} $ then $\frac{dy}{dx} = $

Accepted Answer

$2e^{2x} $

Answer

$2xe^{2x-1}$

Answer

$2e^{x} $

Answer

$e^{2x}$

Question 9

If $ y= ln^2(3x)$ then $\frac{dy}{dx}= $

Accepted Answer

$\frac{2ln(3x)}{x}$

Answer

$\frac{ln(3x)}{x}$

Answer

$\frac{6}{ln(3x)}$

Answer

$6ln(3x)$

Question 10

If $y=(x^2 + e^x)^\frac{1}{2}$  then $\frac{dy}{dx} =$

Accepted Answer

$\frac{2x+e^x}{2(x^2 + e^x)^\frac{1}{2}}$

Answer

$\frac{x+e^x}{(x^2 + e^x)^\frac{1}{2}}$

Answer

$\frac{2x}{2(x^2 + e^x)^\frac{1}{2}}$

Answer

$\frac{1}{2(x^2 + e^x)^\frac{1}{2}}$

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