If y = 3^ x^2 , then dy dx is equal to - Vidyadip

MCQ

If $y = {3^{{x^2}}}$, then ${{dy} \over {dx}}$ is equal to

A
$({x^2}){3^{{x^2} - 1}}$
B
$3{x^2}.2x$
✓
${3^{{x^2}}}.2x.\log 3$
D
$({x^2} - 1).3$

✓

Answer

Correct option: C.

${3^{{x^2}}}.2x.\log 3$

c
(c) Given $y = {3^{{x^2}}}$

$\because \frac{d}{{dx}}({a^x}) = {a^x}{\log _e}a$

$\therefore \frac{{dy}}{{dx}} = {3^{{x^2}}}{\log _e}3\frac{d}{{dx}}({x^2})$

==> $\frac{{dy}}{{dx}} = {3^{{x^2}}}.2x.{\log _e}3$.

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