QExample - 7: HC Verma: Concepts of Physics - Volume 1 Physics and Mathematics Example - 7 Solution: Find {dy}{dx} if y=e^{x}sin~x

\textbf{Problem:}

Find $\frac{dy}{dx}$ if $y = e^x \sin x$.

\textbf{Solution:}

We need to use the product rule for differentiation. The product rule states that if $y = u(x)v(x)$, then:

In our case, we have:

* $u(x) = e^x$

* $v(x) = \sin x$

Now, we find the derivatives of $u(x)$ and $v(x)$:

* $u'(x) = \frac{d}{dx}(e^x) = e^x$

* $v'(x) = \frac{d}{dx}(\sin x) = \cos x$

Now, we apply the product rule:

We can factor out $e^x$:

\textbf{Therefore, the derivative is:}