If y = 3^{x^2},then frac{dy}{dx} is equal to | vedclass

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(C) Given $y = 3^{x^2}$.We know that the derivative of an exponential function is given by $\frac{d}{dx}(a^u) = a^u \cdot \ln(a) \cdot \frac{du}{dx}$,

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) Given $y = 3^{x^2}$.We know that the derivative of an exponential function is given by $\frac{d}{dx}(a^u) = a^u \cdot \ln(a) \cdot \frac{du}{dx}$,where $a$ is a constant and $u$ is a function of $x$.Applying the chain rule:$\frac{dy}{dx} = \frac{d}{dx}(3^{x^2})$$\frac{dy}{dx} = 3^{x^2} \cdot \ln(3) \cdot \frac{d}{dx}(x^2)$Since $\frac{d}{dx}(x^2) = 2x$,we get:$\frac{dy}{dx} = 3^{x^2} \cdot \ln(3) \cdot 2x$Rearranging the terms,we get:$\frac{dy}{dx} = 3^{x^2} \cdot 2x \cdot \log_e 3$.

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

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