Answered: "Find derivatives of the functions defined as follows:..."

College
Calculus and Analysis
Differential Calculus
Derivatives

Dottie Parra

Answered question

2021-10-19

Find derivatives of the functions defined as follows:

y = - 5 e^{4 x^{3}}

Answer & Explanation

averes8

Skilled2021-10-20Added 92 answers

Given,
$y = - 5 e^{4 x^{3}}$
Step 2
Differentiating with respect to x, we get
$\frac{d y}{d x} = - \frac{d}{d x} 5 e^{4} x^{3}$
$= - 5 \cdot \frac{d (e^{4 x^{3}})}{d x}$
$= - 5 \cdot e^{4 x^{3}} \cdot \frac{d (4 x^{3})}{d x} [∵ \frac{d (e^{x})}{d x} = e^{x}]$
$= - 5 \cdot e^{4 x^{3}} \cdot 4 (3 x^{2}) [∵ \frac{d (x^{n})}{d x} = n x^{n - 1}]$
$= - 60 x^{2} e^{4 x^{3}}$

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