Question

Given y=f(u) and u=g(x).y=cos u and u=-x/3.find dy/dx

Answer 1

Given:

Given y=f(u) and u=g(x).y=cos u and u=-x/3.

To find:

Given y=f(u) and u=g(x).y=cos u and u=-x/3. Find dy/dx

Solution:

From given, we have,

y = f(u)

y = cos u

dy/du = - sin u

u = g(x)

u=-x/3

du/dx = -1/3

dy/dx = dy/du × du/dx

= -sin u × (-1/3)

∴ dy/dx = sin u/3

Answer 2

Answer:

If u = -x/3, ------- (1)

& y = cos u

= cos (-x/3) [From (1)]

So, dy/dx = -sin(-x/3) . (-1/3)

= (sin(-x/3))/3