Question

Differentiate (a) with respect to x ( y is a function of x) and (b) with respect to t (x and y are functions of t).

cos πy - 3 sin πx = 1

Answer 1

Step 1 :

(a)

y  is a functions of x, that means .

The function is .

Differentiate implicitly with respect to x.

Apply chain rule : .

The derivative of the function with respect to x :

Step 2 :

(b)

x,y are functions of t, that means and .

The function is .

Differentiate implicitly with respect to t.

Apply chain rule.

The derivative of the function with respect to x:

Solution :

(a)

(b)