Home
Class 12
MATHS
(sinx)^(logx)...

`(sinx)^(logx)`

Text Solution

Verified by Experts

Let `y = (sinx)^logx`
Taking logs both sides,
`logy = logx logsin x `
Differentiating both sides w.r.t. x
`1/y dy/dx = logx(1/sinx)(cosx)+ logsinx (1/x)` `=>1/ydy/dx = logxcotx+logsinx/x`
`=> dy/dx = y( logxcotx+logsinx/x)`
`=> dy/dx = (sinx)^logx( logxcotx+logsinx/x)`, which is the required solution.
Promotional Banner

Similar Questions

Explore conceptually related problems

Differentiate the following functions with respect to x : (e^x+sinx)/(1+logx)

((e^(x) + sinx)/(1+logx))

y=(tanx)^(logx)+(cosx)^(sinx)

Differentiate (e^x+sinx)/(1+logx) with respect to x .

y=(tanx)^(logx)+(cosx)^(sinx) , find dy/dx

Find (dy)/(dx) , if y=(sinx)^(x)+(tan^(-1)x)^(logx)

int(xcosxlogx-sinx)/(x(logx)^2)dx is equal to (A) sinx+c (B) logxsinx+c (C) logx+sinx+c (D) none of these

int(xcosxlogx-sinx)/(x(logx)^2)dx is equal to (A) sinx+c (B) logxsinx+c (C) logx+sinx+c (D) none of these

Differentiate wrt x : (3e^(x)sinx+a^(x)*logx)