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# Calculus Examples

,

Step 1

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

Differentiate using the Quotient Rule which states that is where and .

Differentiate.

Differentiate using the Power Rule which states that is where .

Multiply by .

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

Differentiate using the Power Rule which states that is where .

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

Simplify terms.

Add and .

Multiply by .

Subtract from .

Add and .

Combine and .

Multiply by .

Evaluate the derivative at .

Simplify.

Simplify the denominator.

Add and .

Raise to the power of .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

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.

Combine and .

Multiply .

Combine and .

Multiply by .

Move the negative in front of the fraction.

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

Add to both sides of the equation.

To write as a fraction with a common denominator, multiply by .

Combine and .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Add and .

Reorder terms.

Step 3