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a2linetagadaW

Answered question

2021-09-24

Find the derivatives.

e^{4 x^{3} + \sin (x)} + \ln (5 x^{2} + 3)

Answer & Explanation

Delorenzoz

Skilled2021-09-25Added 91 answers

\frac{d}{d x} [e^{4 x^{3} + \sin (x)} + \ln (5 x^{2} + 3)]

= \frac{d}{d x} [e^{4 x^{3} + \sin (x)}] + \frac{d}{d x} [\ln (5 x^{2} + 3)]

= e^{4 x^{3} + \sin (x)} (12 x^{2} + \cos x) + \frac{10 x + 0}{(5 x^{2} + 3)}

(using chain rule of differentiation and

\frac{d (x^{n})}{d x} = n x^{n - 1}; \frac{d (c o n s \tan t)}{d x} = 0 and \frac{d}{d x} (e^{x}) = e^{x}

)

= e^{4 x^{3} + \sin (x)} (12 x^{2} + \cos x) + \frac{10 x}{(5 x^{2} + 3)}

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