Question

F(x,y)= y^3sin(x) + x^2tan (y)

Answer 1

Answer:

Explanation:

It has x's and y's all over the place! So let us try the letter change trick.

With respect to x we can change "y" to "k":

f(x,y) = k3sin(x) + x2tan(k)

f’x = k3cos(x) + 2x tan(k)

But remember to turn it back again!

f’x = y3cos(x) + 2x tan(y)

Likewise with respect to y we turn the "x" into a "k":

f(x,y) = y^3sin(k) + k^2tan(y)

f’y = 3ysin(k) + k^2sec2(y)

f’y = 3y2sin(x) + x2sec2(y)

But only do this if you have trouble remembering, as it is a little extra work.

Answer 2

F(x ,y) = y^3 sin(x) + x^2 tany

doing partial total derivative of function

f'(x,y) = 3y^2dy/dxsinx + cosx*3y^3 + 3xtany + sec^2y(dy/dx)x^2