Question

Find dy/dx of y=4^lnx

Answer 1

Answer:

$\frac{dy}{dx} = \frac{4^{lnx} . ln4 }{x}$

Step-by-step explanation:

In this question, you will find the differential. We will use following property of derivative.

$\frac{d[a^{f(x)} ]}{dx} = a^{f(x)} . lna . \frac{d[f(x) ]}{dx}$

So for the given equation $y = 4^{lnx}$

taking derivative $\frac{d}{dx\\}$ of both sides

$\frac{dy}{dx} = \frac{d(4^{lnx})}{dx}$

Using the property on right side of the equation

$\frac{dy}{dx} = 4^{lnx} . ln4 . \frac{d(lnx)}{dx} ---(eq 1)$

we know that

$\frac{d(lnx)}{dx} = \frac{1}{x}$

Plug in this value in (eq 1)

$\frac{dy}{dx} = 4^{lnx} . ln4 . \frac{1}{x} \\\frac{dy}{dx} = \frac{4^{lnx} . ln4 }{x}$

which is the final answer