Differentiation I - Normal

Question 1: Differentiate

y

with respect to

x :

y = x^{2} - 5 x

A

\frac{d y}{d x} = x^{2} - 5

B

\frac{d y}{d x} = 2 x - 5

C

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

D

\frac{d y}{d x} = - 5

Question 2: Differentiate

y

with respect to

x :

y = \ln (x)

A

\frac{d y}{d x} = \frac{1}{x}

B

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

C

\frac{d y}{d x} = \ln (\frac{1}{x})

D

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

Question 3: The function f is defined by:

f (x) = 5

. Find

f' (x)

A

f' (x) = 1

B

f' (x) = 0

C

f' (x) = x

D

f' (x) = 5

Question 4: Differentiate

y

with respect to

x :

y = \tan (5 x)

A

\frac{d x}{d y} = \frac{1}{\cos^{2} (5 x)}

B

\frac{d x}{d y} = \frac{1}{\cos^{2} (x)}

C

\frac{d x}{d y} = \frac{5}{\cos^{2} (5 x)}

D

\frac{d x}{d y} = \frac{5}{\cos^{2} (x)}

Question 5: Find the gradient of the function

y = x^{3}

at the point

x_{0} = 2

A

k = 12

B

k = 8

C

k = 4

D

k = 0.5

Question 6: Find the gradient of the function

y = \sin (x)

at the point

x_{0} = π

A

k = 1

B

k = 2

C

k = 0

D

k = - 1

Question 7: Find the gradient of the function

y = x^{2} - x

at the point

x_{0} = 1

A

k = 2

B

k = - 1

C

k = 1

D

k = 0

Question 8: Find the gradient of the function

y = 7 x

at the point

x_{0} = 20

A

k = 7

B

k = 140

C

k = 0

D

k = - 1

Question 9: The function s is defined by:

s (t) = 5 t - 1

, find

s' (t)

A

v = 5

B

v = 7

C

v = 9

D

v = 3

Question 10: The function s is defined by:

s (t) = 7 t + 1

, find

s' (t)

A

v = 9

B

v = 7

C

v = 5

D

v = 6

Test: Differentiation I - Normal

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