Differentiation I - Ambitious

Question 1: Find a derivative of the function

y = t g (x^{2} + 3 x)

A

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

B

y' = \frac{1}{\cos^{2} (x^{2} + 3 x)}

C

y' = \frac{x}{\cos^{2} (x^{2} + 3 x)}

D

y' = \frac{x + 3}{\cos^{2} (x^{2} + 3 x)}

Question 2: Find a derivative of the function

y = e^{(x^{3} + 5)}

A

y' = (x^{3} + 5) e^{(x^{3} + 5)}

B

y' = (3 x^{2} + 5) e^{(x^{3} + 5)}

C

y' = 3 x^{2} e^{(x^{3} + 5)}

D

y' = e^{(x^{3} + 5)}

Question 3: Find a derivative of the function

y = \sqrt{\cos (x)}

A

y' = \frac{1}{\sqrt{\cos (x)}}

B

y' = \frac{\sin (x)}{2 \sqrt{\cos (x)}}

C

y' = \frac{- \sin (x)}{2 \sqrt{\cos (x)}}

D

y' = \frac{1}{2 \sqrt{\cos (x)}}

Question 4: Find a derivative of the function

y = \arcsin (x^{4} + 2 x^{2})

A

y' = \frac{1}{\sqrt{1 - (x^{4} + 2 x^{2})}}

B

y' = \frac{4 x^{3}}{\sqrt{1 - x^{8} - 4 x^{6} + 4 x^{4}}}

C

y' = \frac{1}{\sqrt{1 - x^{8} - 4 x^{6} + 4 x^{4}}}

D

y' = \frac{4 (x^{3} + x)}{\sqrt{1 - x^{8} - 4 x^{6} + 4 x^{4}}}

Question 5: The function s is defined by:

s (t) = t^{2} + t

, find the gradient of the function at the point

t_{0} = 5

A

v = 1

B

v = 5

C

v = 23

D

v = 11

Question 6: The function s is defined by:

s (t) = t^{3} - 2 t

, find the gradient of the function at the point

t_{0} = 1

A

v = 10

B

v = 2

C

v = 1

D

v = 3

Question 7: The function s is defined by:

s (t) = ​ t^{5} - 7 t

, find the gradient of the function at the point

t_{0} = 2

A

v = 66

B

v = 5

C

v = 20

D

v = 25

Question 8: At which point

f' (x_{0}) > 0

?

A

x_{0} = - 3

B

x_{0} = - 4

C

x_{0} = - 5

D

x_{0} = 0

Question 9: At which point

f' (x_{0}) = 0

?

A

x_{0} = 1

B

x_{0} = 5

C

x_{0} = 2

D

x_{0} = 3

Question 10: At which point

f' (x_{0}) < 0

?

A

x_{0} = 10

B

x_{0} = 11

C

x_{0} = 12

D

x_{0} = 8

Test: Differentiation I - Ambitious

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