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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Similar Questions

The derivative of $\log_8(\log_5 x)$ with respect to $x$ is:

If $f(x)=3^x$ and $g(x)=4^x$,then $\frac{f^{\prime}(0)-g^{\prime}(0)}{1+f^{\prime}(0) g^{\prime}(0)}$ is

If $y=\log \sqrt{\frac{1+\sin x}{1-\sin x}}$,then $\frac{d y}{d x}$ at $x=\frac{\pi}{3}$ is

$\frac{d}{dx} \left[ \log \left\{ e^x \left( \frac{x + 2}{x - 2} \right)^{3/4} \right\} \right]$ equals

If $f(x) = \log_{x}(\log x)$,then $f'(x)$ at $x = e$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module