Calculus Derivative

Question

Given f(x,y)=−3x^4+1xy^5+3y^2, find fx(2,2)

Answer 1

f(x ,y) = -3x⁴ + xy⁵+3y²

find δf(x,y) /δx = -3(4)(x^4-1) + (1)(y⁵) + (0) = -12 x³+ y⁵ , fx(2,2) = -12(2)³ +2⁵ = -12(8) + 32 = -96 + 32 = - 64

Answer 2

Take the derivative with respect to x (treat y as a constant). This will give you f_x(x, y)

Then just plug in 2 for x and y to get f_x(2,2)