Exponential derivatives Quiz 1

Question 1

Differentiate $$y = {x^4} + {4^x}$$

Accepted Answer

$$3{x^3} + {4^x}(\ln 4)$$

Answer

$$4{x^3} + (\ln 4)$$

Answer

$$4{x^3} + {4^x}$$

Answer

None of these

Question 2

Differentiate $$y = {x^3}{e^x}$$

Accepted Answer

$${e^x}({x^3} + 3{x^2})$$

Answer

$${x^3} + 3{x^2}$$

Answer

$${e^x}({x^3} + 3{x^3})$$

Answer

None of these

Question 3

Differentiate $$y = \dfrac{{{x^2}}}{{4x}}$$

Accepted Answer

$$\dfrac{1}{4}$$

Answer

$$\dfrac{1}{2}$$

Answer

$$\dfrac{1}{{4x}}$$

Answer

None of these

Question 4

Differentiate $$y = \dfrac{{{e^{2x}} - 1}}{{{e^{2x}} + 1}}$$

Accepted Answer

$$\dfrac{{4{e^{2x}}}}{{{{({e^{2x}} + 1)}^2}}}$$

Answer

$$\dfrac{{{e^{2x}}}}{{{{({e^{2x}} + 1)}^2}}}$$

Answer

$$\dfrac{1}{{{{({e^{2x}} + 1)}^2}}}$$

Answer

None of these

Question 5

Differentiate $$f\left( t \right) = 10t - 8\sqrt[3]{t} + 12{e^t}$$

Accepted Answer

$$10 - \dfrac{8}{3}{t^{\dfrac{{ - 2}}{3}}} + 12{e^t}$$

Answer

$$10 - \dfrac{8}{3}{t^{\dfrac{2}{3}}} + 12{e^t}$$

Answer

$$10 - \dfrac{8}{3}{t^{\dfrac{1}{3}}} + 12{e^t}$$

Answer

None of these