Finding f inverse prime at a point c

[k3k3]

Homework Statement

Assume the function f defined by f(x)=5x+sin(πx) is strictly increasing on ℝ. Find (f$^{-1}$)'(10)

Homework Equations

Let I and J be be intervals and let f:I->J be a continuous, strictly monotone function. If f is differentiable at c and if f'(c)≠0, then (f$^{-1}$) is differentiable at f(c) and (f$^{-1}$)'(f(c))= 1/f'(c)

The Attempt at a Solution

It is clear f is continuous and differentiable on ℝ.
=> f'(x) = 5+πcos(πx)


Finding when f(x)=10,
10 = 5x+sin(πx) => x=2

Then (f$^{-1}$)'(f(2))=1/f'(2) = 1/(5+πcos(2π)) = 1/(5+(π))

Is this how to do it, or do I use f(10) instead of finding when f(x) is 10?

 

[haruspex]

That all looks right. If you think of it as y = f(x) and x = f^-1(y), the 10 is a value of y, not of x, so f(10) and f'(10) would not be relevant.