Finding First and Second Derivatives - High School Math

Card 0 of 2

Question

Find the second derivative of f(x).

$f(x)=\frac{1}{4} e^{2x}-cosx$

Answer

First we should find the first derivative of . Remember the derivative of $e^{2x}$ is $2e^{2x}$ and the derivative of is :

$f'(x)=\frac{1}{2}e^{2x}+sinx$

The second derivative is just the derivative of the first derivative:

$f''(x)=e^{2x}+cosx$

Compare your answer with the correct one above

Question

Find the derivative of the function

.

Answer

We can use the Chain Rule:

Let , so that .

$\frac{df}{dx}=\frac{df}{du}.\frac{du}{dx}=(4u^3-3u^2+2u)\cdot sec^2x=(4tan^3x-3tan^2x+2tanx)\cdot sec^2x$

Compare your answer with the correct one above

Tap the card to reveal the answer