Enter a problem...

# Calculus Examples

,

Step 1

Differentiate both sides of the equation.

Differentiate the left side of the equation.

By the Sum Rule, the derivative of with respect to is .

Evaluate .

Since is constant with respect to , the derivative of with respect to is .

Differentiate using the Power Rule which states that is where .

Multiply by .

Evaluate .

Differentiate using the chain rule, which states that is where and .

To apply the Chain Rule, set as .

Differentiate using the Power Rule which states that is where .

Replace all occurrences of with .

Rewrite as .

Reorder terms.

Since is constant with respect to , the derivative of with respect to is .

Reform the equation by setting the left side equal to the right side.

Solve for .

Subtract from both sides of the equation.

Divide each term in by and simplify.

Divide each term in by .

Simplify the left side.

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of .

Cancel the common factor.

Divide by .

Simplify the right side.

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

Replace with .

Evaluate at and .

Replace the variable with in the expression.

Replace the variable with in the expression.

Move the negative one from the denominator of .

Multiply .

Multiply by .

Multiply by .

Step 2

Use the slope and a given point to substitute for and in the point-slope form , which is derived from the slope equation .

Simplify the equation and keep it in point-slope form.

Solve for .

Simplify .

Rewrite.

Simplify by adding zeros.

Apply the distributive property.

Multiply by .

Move all terms not containing to the right side of the equation.

Subtract from both sides of the equation.

Subtract from .

Step 3