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## Homework Statement

Find: ∂f/∂x

f(r,θ)=rsin^2(θ), x=rcosθ, y=rsinθ

## The Attempt at a Solution

∂f/∂r=sin^2θ ∂r/∂x=-cosθ/x

∂f/∂θ=2*r*cosθ*sinθ ∂θ/∂x=-1/sqrt(1-(x^2)/(r^2)

∂f/∂x = -sin^2θcosθ/x^2 + -2*r*cosθ*sinθ/sqrt(1-(x^2)/(r^2)

∂f/∂x = -y-sqrt(x^2+y^2) / (x^2+y^2)^3/2

THE ANSWER IN THE BACK OF THE BOOK IS :

∂f/∂x = -xy^2 / (x^2+y^2)^3/2