Find the derivative of 7^x w. r.t. x^7. - Vidyadip

Question

Find the derivative of $7^x$ w. r.t. $x^7$.

✓

Answer

Let : $u=7^x$ and $v=x^7$, then we have to find $\frac{d u}{d v}$.
$
\therefore \frac{d u}{d v}=\frac{\frac{d u}{d x}}{\frac{d v}{d x}}
$
Now, $u=7^x$
Differentiate w.r.t. $x$
$
\frac{d u}{d x}=\frac{d}{d x}\left(7^x\right)=7^x \log 7 \ldots
$
And, $v=x^7$
Differentiate w.r. t. $x$
$
\frac{d v}{d x}=\frac{d}{d x}\left(x^7\right)=7 x^6
$
Substituting (II) and (III) in (I) we get,
$
\therefore \frac{d u}{d v}=\frac{7^x \log 7}{7 x^6}
$

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