Question

write all the steps........​

Answer 1

Answer:

Find the attachement

Step-by-step explanation:

Hi

Hope this helps you

Answer 2

Step-by-step explanation:

Given: log(logx)

1st Derivative:

$\Rightarrow \frac{d}{dx}(log(logx))$

Let u = logx, then f = log u.

$\Rightarrow \frac{d}{du}(logu) \frac{d}{dx}(logx)$

$\Rightarrow \frac{1}{u} * \frac{1}{x}$

$\Rightarrow \frac{1}{logx} * \frac{1}{x}$

$\Rightarrow \frac{1}{xlogx}$

2nd Derivative:

$\Rightarrow \frac{d}{dx}(\frac{dy}{dx}) = \frac{d}{dx}(\frac{1}{xlogx})$

$\Rightarrow \frac{d^2y}{dx} = \frac{0 * xlogx-\frac{d(xlogx)}{dx}}{(xlogx)^2}$

$\Rightarrow \frac{d^2y}{dx} = \frac{-\frac{d(xlogx)}{dx}}{(xlogx)^2}$

$\Rightarrow \frac{d^2y}{dx} = \frac{[\frac{d}{dx}(x).logx+\frac{d}{dx}logx*x]}{(xlogx)^2}$

$\Rightarrow \frac{d^2y}{dx} = \frac{-[1.logx+\frac{1}{x} *x]}{(xlogx)^2}$

$\Rightarrow \boxed{\frac{d^2y}{dx} = \frac{-[logx+1]}{(xlogx)^2}}$

Hope it helps!