Question

if y =e^3 logx Show that dy/dx=3x^2

Answer 1

Answer:

$\frac{dy}{dx}=3x^2$

Step-by-step explanation:

Given : $y=e^{3\log x}$

To find : Show that $\frac{dy}{dx}=3x^2$ ?

Solution :

We have given,

$y=e^{3\log x}$

Apply logarithmic property, $a\log x=\log x^a$

$y=e^{\log x^3}$

Again applying logarithmic property,$e^{\log x}=x$

$y=x^3$

Derivate w.r.t x,

$\frac{dy}{dx}=3x^2$