Question

Second implicit derivative calculator

A) Solving linear equations
B) Finding the second derivative of implicit functions
C) Computing definite integrals
D) Evaluating trigonometric functions

Answer 1

To find the second derivative of an implicit function, we differentiate both sides of the equation with respect to the variable and apply the chain rule.

Step-by-step explanation:

The second derivative of an implicit function can be found using the chain rule. Let's say we have an implicit function F(x, y) = 0, where both x and y are variables. To find the second derivative of y with respect to x, we differentiate both sides of the equation with respect to x and apply the chain rule.

For example, let's say we have the implicit function x^2 + y^2 = 1. To find the second derivative of y with respect to x, we differentiate both sides of the equation:

2x + 2yy' = 0

Next, we differentiate the equation again with respect to x to find the second derivative of y:

2 + 2yy'' + 2(y')^2 = 0

Finally, we solve the equation for y'' to get the second derivative of y with respect to x.