Higher order derivatives Quiz 1

Question 1

What is the second derivative of the function: $$f\left( x \right) = {x^3} + {e^x} + \cos x$$?

Accepted Answer

$$6{x^{}} + {e^x} - \cos x$$

Answer

$$3{x^2} + {e^x} + \sin x$$

Answer

$$6{x^{}} + {e^x} + \cos x$$

Answer

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

Question 2

The position of the particle is given by $$x = 3{t^2} - 2$$. Its instantaneous velocity Is:

Accepted Answer

$$6t$$

Answer

$$3{t^2}$$

Answer

$$6t - 2$$

Answer

$$6$$

Question 3

If $$x = 3{t^3} + 5{t^2} - 2t$$ is the position of an object, what will be its acceleration at $$t = 2\operatorname{s} $$.

Accepted Answer

$$46m/{s^2}$$

Answer

$$10m/{s^2}$$

Answer

$$56m/{s^2}$$

Answer

$$76m/{s^2}$$

Question 4

Determine $$y'''$$ for $$y = \dfrac{1}{4}{x^{\dfrac{1}{2}}}$$.

Accepted Answer

$$\dfrac{1}{{32}}{x^{ - \dfrac{5}{2}}}$$

Answer

$$ - \dfrac{1}{{32}}{x^{ - \dfrac{5}{2}}}$$

Answer

$$\dfrac{1}{{16}}{x^{ - \dfrac{3}{2}}}$$

Answer

$$ - \dfrac{1}{{16}}{x^{ - \dfrac{3}{2}}}$$

Question 5

If $$f\left( x \right) = \ln \left( {{x^2}\sqrt x } \right)$$, what is the value of $$f''\left( x \right)$$

Accepted Answer

$$ - \dfrac{5}{{2{x^2}}}$$

Answer

$$\dfrac{5}{{2x}}$$

Answer

$$ - \dfrac{5}{{2x}}$$

Answer

$$\dfrac{5}{{2{x^2}}}$$