Find y'' by implicit differentiation. x2 + 5y2 = 5

The expression for is .

Further explanation:

Given:

The expression is .

Concept used:

Implicit Differentiation is used to differentiate the function which contains as a function of or is a function of .

The implicit differentiation is useful to obtain the expression of and .

The chain rule is the best tool in the implicit differentiation of the any expression.

The quotient rule of differentiation  is as follows:

Calculation:

Differentiate the equation with respect to .

Arrange the above equation to obtain the expression of .

Simplified the above equation to obtain the value of .

Again differentiate the above equation with respect to the as follows:

Apply the quotient rule of differentiation to obtain the value of .

Substitute in the above equation.

Substitute in the above equation.

Therefore, the expression of by the implicit differentiation is .

Learn more:

1. Function:

2. Quadratic equation:

Answer details:

Grade: Senior school.

Subject: Mathematics.

Chapter: Differentiation.

Keywords: Implicit differentiation, explicit differentiation, chain rule, quotient rule of differentiation, the value of y', the value of y'', with respect to x,  chain rule.

8+10

step-by-step explanation:

you multiply 4 by 2 and 5 by 2