Determine the derivative of the function (² = square):

Question

a) y = (x² + x - 1)Sin²x

b) y = (x² + 1)/Sin²x

Answer 1

chain rule:
d/dx sin^2 x = 2(sinx)(cosx) = sin2x

a)
y = (x^2+x-1)sin^2 x
y' = (2x+1)sin^2 x + (x^2+x-1)sin2x

b)
y = (x^2+1)/sin^2 x
y = (2x*sin^2 x - (x^2+1)*2*sinx*cosx]/sin^4 x
= [2x*sinx - (x^2+1)*cosx]/sin^3 x

Answer 2

Thank you Steve