Find the first partial derivatives

Question

a. f(x,y)=e^(xy)ln(y)

b. f(x,y)=x^y

c. f(x,y,z)=xy sin^(-1)(yz)

Answer 1

(a) ∂f/∂x=yeˣʸln(y), ∂f/∂y=eˣʸ/y+xln(y)eˣʸ.

(b) f(x,y)=xʸ=e^(yln(x)),

∂f/∂x=yxʸ⁻¹, ∂f/∂y=ln(x)xʸ.

(c) ∂f/∂x=ysin⁻¹(yz),

∂f/∂y=xyz/√(1-y²z²)+xsin⁻¹(yz),

∂f/∂z=xy²/√(1-y²z²).