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

If f(x)=xtan^(-1)x , then f'(1) is

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

Find the derivative of e^(sqrt(x)) w.r.t. x using the first principle.

Find the derivative of sqrt(4-x) w.r.t. x using the first principle.

Differentiate f(x)=e^(2x) from first principles.

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

If f^(prime)(x)=1/(-x+sqrt(x^2+1)) and f(0)=(1+sqrt(2))/2 then f(1) is equal to- (a) log"(sqrt(2)+1) (b) 1 (c) 1+sqrt(2) (d) none of these

If f((x+2y)/3)=(f(x)+2f(y))/3AAx ,y in Ra n df^(prime)(0)=1,f(0)=2, then find f(x)dot

If y=f(x^3),z=g(x^5),f^(prime)(x)=tanx ,a n dg^(prime)(x)=secx , then find the value of (lim)_(xvec0)(((dy)/(dz)))/x

Find the range of f(X) = tan^(-1)x-(1)/(2)log_(e)x in (1)/(sqrt(3)),(sqrt(3))