Question

Find the derivative: f(x)=tan alt="(x^{2} +5)" align="absmiddle" class="latex-formula">

Answer 1

Answer:

$2x \sec^2 (x^2 + 5)$

Step-by-step explanation:

$f(x) = \tan (x^2 + 5)$

$\dfrac{d}{dx} \tan u = \sec^2 u \dfrac{d}{dx} u$

$\dfrac{d}{dx} \tan (x^2 + 5) = \sec^2 (x^2 + 5) \dfrac{d}{dx} (x^2 + 5)$

$\dfrac{d}{dx} \tan (x^2 + 5) = [\sec^2 (x^2 + 5)]2x$

$\dfrac{d}{dx} \tan (x^2 + 5) = 2x \sec^2 (x^2 + 5)$