Differentiate the following w.r.t. x. : x^5+3 x^4 - Vidyadip

Question

Differentiate the following w.r.t. x. : $x^5+3 x^4$

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Answer

Let $y=x^5+3 x^4$
Differentiating w.r.t. $x$, we get
$
\begin{aligned}
\frac{\mathrm{d} y}{\mathrm{~d} x} & =\frac{\mathrm{d}}{\mathrm{d} x}\left(x^5+3 x^4\right) \\
& =\frac{\mathrm{d}}{\mathrm{d} x} x^5+3 \frac{\mathrm{d}}{\mathrm{d} x} x^4 \\
& =5 x^4+3\left(4 x^3\right) \\
\frac{\mathrm{d} y}{\mathrm{~d} x} & =5 x^4+12 x^3
\end{aligned}
$

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