Free Printable DIFFERENTIATION OF EXP, LOG AND TRIGO FUNCTIONS

1.

$\frac{\text{d}}{\text{d}x}\left(e^{\left(3x+2\right)}\right)$

a)

$3e^{\left(3x+2\right)}$

b)

$3x\left(2x+1\right)e^{\left(3x+2\right)}$

c)

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

d)

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

2.

$\frac{\text{d}}{\text{d}x}\left(\frac{1}{e^{3x}}+4x^5\right)$

a)

$20x^4-\frac{3}{e^{3x}}$

b)

$\frac{1}{e^{3x}}+20x^4$

c)

$\frac{1}{e^{3x}}+30x^6$

d)

$30x^6-\frac{6x}{e^{3x}}$

3.

$\frac{\text{d}}{\text{d}x}\left(\frac{2x^3}{e^{2x}}\right)$

a)

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

b)

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

c)

$-\frac{2x^4\left(3x-4\right)}{e^{2x}}$

d)

$\frac{2x^4\left(3x-4\right)}{e^{2x}}$

4.

$\frac{\text{d}}{\text{d}x}\left(\sqrt{e^x+6}\right)$

a)

$\frac{e^x}{2\sqrt{e^x+6}}$

b)

$\frac{e^x+12x^2}{2\sqrt{e^x+6}}$

c)

$\frac{3\sqrt{e^x+6}}{2e^x}$

d)

$\frac{3e^x\sqrt{e^x+6}}{2}$

5.

$\frac{\text{d}}{\text{d}x}\left(\frac{e^{3x}}{\sin\left(2x\right)}\right)$

a)

$\frac{e^{3x}\left(3\sin\left(2x\right)-2\cos\left(2x\right)\right)}{\sin^2\left(2x\right)}$

b)

$\frac{e^{3x}\left(2\cos\left(2x\right)-3\sin\left(2x\right)\right)}{\sin^2\left(2x\right)}$

c)

$\frac{e^{3x}\left(3\sin\left(2x\right)+2\cos\left(2x\right)\right)}{\sin^2\left(2x\right)}$

d)

$\frac{e^{3x}\left(\sin\left(2x\right)-2\cos\left(2x\right)\right)}{\sin^2\left(2x\right)}$

6.

$\frac{\text{d}}{\text{d}x}\left(4e^{\left(3x-1\right)}\cos x\right)$

a)

$4e^{\left(3x-1\right)}\left(3\cos x-\sin x\right)$

b)

$4e^{\left(3x-1\right)}\left(3\cos x+\sin x\right)$

c)

$4e^{\left(3x-1\right)}\left(\cos x-\sin x\right)$

d)

$4e^{\left(3x-1\right)}\left(\cos x+\sin x\right)$

7.

$\frac{\text{d}}{\text{d}x}\left(x^2e^{\left(x^2+3\right)}\right)$

a)

$2x\left(x^2+1\right)e^{\left(x^2+3\right)}$

b)

$x\left(x^2+2\right)e^{\left(x^2+3\right)}$

c)

$3x^3\left(x^2+1\right)e^{\left(x^2+3\right)}$

d)

$2\left(x^2+1\right)e^{\left(x^2+3\right)}$

8.

differentiate\ \cos\left(\log x\ +\ e^x\right)

a)

$-\frac{1}{x}\sin\left(\log x\ +\ e^x\right)\left(1+xe^x\right)$

b)

$\frac{1}{x}\sin\left(\log x\ +\ e^x\right)\left(1+xe^x\right)$

c)

$-\frac{e^x}{x}\sin\left(\log x\ +\ e^x\right)\left(1+xe^x\right)$

d)

$-\frac{1}{x}\cos\left(\log x\ +\ e^x\right)\left(1+xe^x\right)$

9.

differentiate\ 5^{\sin x}

a)

$5^{\sin x}\cos x.\ \log5$

b)

$5^{\sin x}\cos x.\ \log e$

c)

$5^{\cos x}\cos x.\ \log5$

d)

None of these

10.

Differentiate

y=\frac{1}{3}\ln x

a)

3/x

b)

1/x

c)

x/3

d)

1/3x

11.

Find $\frac{dy}{dx}$ for $y=\ln\left(\frac{2x+1}{1-2x}\right)$ .

a)

$\frac{2}{2x+1}-\frac{2}{1-2x}$

b)

$\frac{2}{2x+1}+\frac{2}{1-2x}$

c)

$\frac{2}{2x-1}+\frac{2}{1-2x}$

d)

$\frac{2}{2x+1}+\frac{2}{1+2x}$

12.

The derivative of $x\cos2x$

a)

$2x\sin2x+\cos2x$

b)

$-2x\sin2x+\cos2x$

c)

$\cos2x+4\sin2x$

d)

$2x\cos2x$

13.

Find $\frac{dy}{dx}$ for $y=\tan^4\left(2x+1\right)$ .

a)

$8\tan^4\left(2x+1\right)\sec^2\left(2x+1\right)$

b)

$2\tan^3\left(2x+1\right)\sec^2\left(2x+1\right)$

c)

$4\tan^3\left(2x+1\right)\sec^2\left(2x+1\right)$

d)

$8\tan^3\left(2x+1\right)\sec^2\left(2x+1\right)$

14.

Differentiating $\frac{\left(e^{2x}-e^x\right)^2}{e^x}$ yields:

a)

$3e^{3x}+e^x$

b)

$3e^{3x}-4e^{2x}+e^x$

c)

$e^{3x}-e^{2x}+e^x$

d)

$e^{3x}+e^x$

e)

$\frac{1}{3}e^{3x}-e^{2x}+e^x$

15.

$\frac{d^2y}{dx^2}\ is\ equal\ to$

a)

$\frac{d}{dx}\left(\frac{\text{d}y}{\text{d}x}\right)$

b)

$\frac{d}{dx}\left(\frac{\text{d}x}{\text{d}y}\right)$

c)

$\frac{1}{\left(\frac{d^2x}{dy^2}\right)}$

d)

$\frac{d}{dy}\left(\frac{\text{d}x}{\text{d}y}\right)$

DIFFERENTIATION OF EXP, LOG AND TRIGO FUNCTIONS

Total questions: 15

Worksheet time: 3hrs 30mins

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