Question

Find dy/dx

Answer 1

\[\Huge y=e^{9\sqrt{x}}\]

Answer 2

By the chain rule:\[f(x)=e^{g(x)}~~\Rightarrow~~f'(x)=e^{g(x)}\cdot g'(x)\]

Answer 3

In this case, \(g(x)=9\sqrt x\), so \(g'(x)=\dfrac{9}{2\sqrt x}\).

Also, \(f'(x)=\dfrac{dy}{dx}\). Just a notation preference.

Answer 4

So it'd pretty much be..
\[\Huge \frac{9*e^{9\sqrt{x}}}{2\sqrt{x}}\]

Answer 5

correct @Luigi0210

Answer 6

Yes! Thank you for the clarification~