Differentiation - Ambitious

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Question 1: Find the gradient of a straight line whith the points

P (5,3)

and

Q (8,12)

2

3

1

- 1

Question 2: Find

\frac{d y}{d x}

for

y = 5 x^{3} - 2 x^{2} + 7 x - 15

\frac{d y}{d x} = - x^{2} + x - 1

\frac{d y}{d x} = 15 x^{3} - 4 x^{2} + 7 x - 15

\frac{d y}{d x} = 125 x^{2} - 4 x + 49

\frac{d y}{d x} = 15 x^{2} - 4 x + 7

Question 3: Find

\frac{d^{2} y}{d x^{2}}

for

y = 4 x^{4} - 3 x^{3} - 6 x^{2} + x

\frac{d^{2} y}{d x^{2}} = 48 x^{2} - 18 x - 12

\frac{d^{2} y}{d x^{2}} = 16 x^{2} - 9 x - 12

\frac{d^{2} y}{d x^{2}} = 8 x^{2} - 6 x - 8

\frac{d^{2} y}{d x^{2}} = 16 x^{3} - 9 x^{2} - 12 x + 1

Question 4: Find

\frac{d y}{d x}

x = 3

for

y = \frac{1}{2} x^{4} - \frac{3}{4} x^{3} + 17

\frac{d y}{d x} = 33.75

\frac{d y}{d x} = 18

\frac{d y}{d x} = 23.25

\frac{d y}{d x} = 27.125

Question 5: Find

\frac{d y}{d x}

y = e^{x} \cos x

\frac{d y}{d x} = e^{x} (\cos x - \sin x)

\frac{d y}{d x} = - e^{x} (\cos x - \sin x)

\frac{d y}{d x} = \cos x - \sin x

\frac{d y}{d x} = e^{x} (\sin x - \cos x)

Question 6: Find

\frac{d y}{d x}

y = 7 x^{4} \sin x

\frac{d y}{d x} = 7 x^{3} (x \cos x + 4 \sin x)

\frac{d y}{d x} = 21 x^{2} (x \cos x - 4 \sin x)

\frac{d y}{d x} = x^{3} (7 x \cos x + \sin x)

\frac{d y}{d x} = 7 x^{4} (\cos x + 4 \sin x)

Question 7: Find

\frac{d y}{d x}

y = \frac{\sin x}{x^{5}}

\frac{d y}{d x} = \frac{x \cos x - 5 \sin x}{x^{6}}

\frac{d y}{d x} = \frac{5 \cos x - x \sin x}{x^{5}}

\frac{d y}{d x} = 5 \frac{\cos x}{x^{4}}

\frac{d y}{d x} = 5 \frac{\cos x - \sin x}{x^{4}}

Question 8: Find

\frac{d y}{d x}

y = \frac{e^{x}}{\tan x}

\frac{d y}{d x} = \frac{e^{x}}{\sec x}

\frac{d y}{d x} = \frac{e^{x} (\sin x - \cos x)}{\tan^{2} x}

\frac{d y}{d x} = \frac{e^{x} (\tan x - \sec^{2} x)}{\tan^{2} x}

\frac{d y}{d x} = \frac{e^{x}}{\sec^{2} x}

Question 9: Find

\frac{d y}{d x}

y = {(2 x + 7)}^{5}

\frac{d y}{d x} = 15 x^{4}

\frac{d y}{d x} = 10 {(2 x + 7)}^{4}

\frac{d y}{d x} = {(2 x + 7)}^{4}

\frac{d y}{d x} = 5 {(2 x + 7)}^{4}

Question 10: Find

\frac{d y}{d x}

y = 6 e^{\cos x}

\frac{d y}{d x} = 6 \cos x e^{\cos x}

\frac{d y}{d x} = - 6 \sin e^{\cos x}

\frac{d y}{d x} = - 6 \cos e^{\sin x}

\frac{d y}{d x} = - 6 \sin x e^{\cos x}

Test: Differentiation - Ambitious