If the function `f(x)=7^(x^3+3x)` `(x gt 0)` , then find the value of `f'(x)`.

g(x) is a inverse function of f.g(x)=x^(3)+e^((x)/(2)) then find the value of f'(x)

If f(x)=x^(3)+2x , then find the value of f(3) .

If f(x)=x^(3)-(1)/(x^(3)) , then find the value of f(x)+f(-x) .

If a differentiable function f defined for x gt0 satisfies the relation f(x^(2))=x^(3),x gt 0 , then what is the value of f'(4)?

If f(x ) = x^3 - 1/x^3 , then find the value of f(x) + f( 1/x )

If the function f (x) = {{:(3,x lt 0),(12, x gt 0):} then lim_(x to 0) f (x) =

Let f be a function satisfying the functional equation f(x)+2f((2x+1)/(x-2))=3x,x!=2 then find the value of |(f(3))/(f(7))|

Given the function f(x) = x^(2) e^(-2x), x gt 0 . Then f(x) has the maximum value equal to

Consider the function f(x)=1/x^(2) for x gt 0 . To find lim_(x to 0) f(x) .