Suppose that x and y are both differentiable functions of t and are related by the given equation. Use implicit differentiation with respect to t to determine StartFraction dy Over dt EndFraction dy dt in terms of x, y, and StartFraction dx Over dt EndFraction dx dt.

Let z = f(x, y) where f(x, y) =0 then the implicit function is

Example:-

Step-by-step explanation:

Partial differentiation:-

   Exists , is said to be partial derivative or Partial differentiational co-efficient of Z or f(x, y)with respective to x.

It is denoted by δ z / δ x or δ f / δ x

   Exists , is said to be partial derivative or Partial differentiational co-efficient of Z or f(x, y)with respective to y

It is denoted by δ z / δ y or δ f / δ y

Implicit function:-

Let z = f(x, y) where f(x, y) =0 then the implicit function is

The total differential co-efficient

d z = δ z/δ x +   δ z/δ y

Implicit differentiation process

Example :  

solution:-

differentiate both sides of the equation with respective to 'x'

move all d y/dx terms to the left side, and all other terms to the right side

Taking common d y/dx

answer: it's a

step-by-step explanation: