Free Printable 3.1 Differentiation of exponential functions

1.

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

a)

$e^x$

b)

$-e^x$

c)

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

d)

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

2.

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

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)

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

3.

$\frac{\text{d}}{\text{d}y}\left(x^3-2xe^x\right)$

a)

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

b)

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

c)

$3x^2-2xe^x\left(2x+1\right)$

d)

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

4.

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

a)

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

b)

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

c)

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

d)

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

5.

$\frac{\text{d}}{\text{d}y}\left(e^{\left(2x+1\right)}\right)^2$

a)

$4e^{\left(4x+2\right)}$

b)

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

c)

$e^{\left(4x+2\right)}\left(8x^2+2x\right)$

d)

$\frac{\left(8x^2+2x\right)}{e^{\left(4x+2\right)}}$

6.

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

a)

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

b)

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

c)

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

d)

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

7.

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

a)

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

b)

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

c)

$3\left(e^x+4x^2\right)\left(e^x+2x\right)^2$

d)

$4\left(e^x+2\right)^4$

8.

$\frac{\text{d}}{\text{d}y}\left(3xe^{4x}\right)$

a)

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

b)

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

c)

$3\left(2x^2+1\right)e^{4x}$

d)

$3\left(8x^2+1\right)e^{4x}$

9.

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

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)

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

10.

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

a)

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

b)

$\frac{5e^{5x}\left(5x+4\right)}{\left(5x+3\right)^2}$

c)

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

d)

$\frac{5e^{5x}\left(4-5x\right)}{\left(5x+3\right)^2}$

3.1 Differentiation of exponential functions

Total questions: 10

Worksheet time: 39mins

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