Differentiation Rules

Differentiation of Inverse Functions


Given the function f(x)=3x2+2x+1f(x)=3x^2+2x+1 defined only for x>0,x > 0, what is the value of (f1)(6)?\left(f^{-1}\right)'(6)?

Given the function f(x)=5lnx4,f(x)=5\ln\frac{x}{4}, what is the value of (f1)(ln32)?\left(f^{-1}\right)'(\ln32)?

If f(x)=5sin13x,f(x)=5\sin^{-1}3x, what is the value of f(36)?f'\left(\frac{\sqrt{3}}{6} \right)?

Given f(x)=5x+1xf(x)=5x+\frac{1}{x} in the domain x>12, x > \frac{1}{2} , what is (f1)(6)?\left(f^{-1}\right)'(6)?

Let f(x)f(x) be a differentiable function and let g(x)g(x) be the inverse of f(x)f(x). If f(2)=6f(2)=6 and f(2)=15,f'(2)=\frac{1}{5}, what is the value of g(6)?g'(6)?


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