derivatives: Find the value of (f o g)'(x) at the given valu

[xc630]

Hello I need some help with the following problem:

find the value of (fog)' at the given value of x

I am just going to use the variables y and u instead of f(u) or g(x).

y = cot ((pi * u) /10)

u= 5 SQRT(x) x =1

so I plugged in 1 and u = 5

i know I need to find dy/du and multiply it by du/dx and then plug in the numbers. However I am haivng trouble finding dy/du, the derivative of cot ((pi*u)/10). Would it be -csc^2 (pi*u/10) . For du/dx I got 5/2 x^-1/2

 

[galactus]

You're correct with \(\displaystyle \L\\\frac{d}{dx}[cot(x)]=-csc^{2}(x)\)