Question

Differentiation of y is equal to e power x into tan inverse of x

Answer 1

Answer:

HEYY...

Note: y2 represents second order derivative i.e.and y1 = dy/dx

Given,

y = etan–1x ……equation 1

to prove : (1+x2)y2+(2x–1)y1=0

We notice a second order derivative in the expression to be proved so first take the step to find the second order derivative.

Let’s find

As,

So, lets first find dy/dx



Using chain rule we will differentiate the above expression

Let t = tan–1 x =>

And y = et

….equation 2

Again differentiating with respect to x applying product rule:

Using chain rule we will differentiate the above expression-

Using equation 2 :

∴ (1+x2)y2+(2x–1)y1=0 ……proved.

hope it helps..