Question

question
find the derivative of (f(x)= - 6\tan(x)+x^{2}).
provide your answer below:
(f(x)=square)

Explanation:

Step1: Recall derivative rules

The derivative of a sum of functions is the sum of the derivatives. Also, recall $\frac{d}{dx}(\tan(x))=\sec^{2}(x)$ and $\frac{d}{dx}(x^{n}) = nx^{n - 1}$.

Step2: Differentiate $- 6\tan(x)$

Using the constant - multiple rule and the derivative of $\tan(x)$, we have $\frac{d}{dx}(-6\tan(x))=-6\frac{d}{dx}(\tan(x))=-6\sec^{2}(x)$.

Step3: Differentiate $x^{2}$

Using the power rule $\frac{d}{dx}(x^{n})=nx^{n - 1}$ with $n = 2$, we get $\frac{d}{dx}(x^{2})=2x$.

Step4: Find $f'(x)$

$f'(x)=\frac{d}{dx}(-6\tan(x)+x^{2})=\frac{d}{dx}(-6\tan(x))+\frac{d}{dx}(x^{2})=-6\sec^{2}(x)+2x$.

Answer:

$-6\sec^{2}(x)+2x$