Question

S=xy+64/y+64/x. Partially differentiate it w.r.t x and y with steps.

Answer 1

partial derivatives with respect to a variable means that u take the deriv while treating the rest of the variables constant

Answer 2

for fy(x,y), treat x as a constant, so S = x + (-64/y^2) + 0

Answer 3

dang it, messed up... for fx(x,y) it's S = y + 0 + (-64/x^2)

Answer 4

How did (-64/y^2) happen?

Answer 5

basic single variable calculus, use the power rule.

Answer 6

can you elaborate it with steps?

Answer 7

sure :). Ok so let's get the derivative of the function with respect to y. In this case, x is held as a constant, so the third term in the function will be 0. You get this, right?

Answer 8

the first term, xy, when differentiate against y, becomes x

Answer 9

so, the second term 64/y, can be written as 64*y^-1. According to the power rule (d/dx) x^n = nx^(n-1). so (d/dy) 64*y^-1 = (-1)*64y^-1-1= -64y^-2 = -64/y^2

Answer 10

do you get it?

Answer 11

Yea got it! Thankyou :)