If `f(x)=|x|^(|sinx|),` then find `f^(prime)(-pi/4)`

If f(x)=x|x|, then prove that f^(prime)(x)=2|x|

If f(x)=sqrt(1-sin2x) , then f^(prime)(x) is equal to (a) -(cosx+sinx),forx in (pi/4,pi/2) (b) cosx+sinx ,forx in (0,pi/4) (c) -(cosx+sinx),forx in (0,pi/4) (d) cosx-sinx ,forx in (pi/4,pi/2)

If f(x)=x+sinx , then find the value of int_pi^(2pi)f^(-1)(x)dxdot

If f(x)=cosxdotcos2xdotcos4xdotcos8xdotcos16 x , then find f^(prime)(pi/4)dot

If f(x)=xtan^(-1)x , find f^(prime)(sqrt(3)) using the first principle.

Let f(x) be differentiable for real x such that f^(prime)(x)>0on(-oo,-4), f^(prime)(x) 0on(6,oo), If g(x)=f(10-2x), then the value of g^(prime)(2) is a. 1 b. 2 c. 0 d. 4

Let f(x y)=f(x)f(y)AAx , y in Ra n df is differentiable at x=1 such that f^(prime)(1)=1. Also, f(1)!=0,f(2)=3. Then find f^(prime)(2)dot

f(x)=x^(4)-6x^(2) find f'(x) .

Let f(x),xgeq0, be a non-negative continuous function. If f^(prime)(x)cosxlt=f(x)sinxAAxgeq0, then find f((5pi)/3)

If fx=x+sinx , then int_(pi)^(2pi)f^(-1)(x)dx is equal to