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# Calculus Examples

,

Step 1

Step 1.1

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

Step 1.2

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

Step 1.3

Differentiate.

Step 1.3.1

Differentiate using the Power Rule which states that is where .

Step 1.3.2

Multiply by .

Step 1.3.3

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

Step 1.3.4

Differentiate using the Power Rule which states that is where .

Step 1.3.5

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

Step 1.3.6

Simplify terms.

Step 1.3.6.1

Add and .

Step 1.3.6.2

Multiply by .

Step 1.3.6.3

Subtract from .

Step 1.3.6.4

Simplify the expression.

Step 1.3.6.4.1

Subtract from .

Step 1.3.6.4.2

Move the negative in front of the fraction.

Step 1.3.6.4.3

Multiply by .

Step 1.3.6.5

Combine and .

Step 1.3.6.6

Move the negative in front of the fraction.

Step 1.4

Evaluate the derivative at .

Step 1.5

Simplify.

Step 1.5.1

Simplify the denominator.

Step 1.5.1.1

Subtract from .

Step 1.5.1.2

One to any power is one.

Step 1.5.2

Simplify the expression.

Step 1.5.2.1

Divide by .

Step 1.5.2.2

Multiply by .

Step 2

Step 2.1

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

Step 2.2

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

Step 2.3

Solve for .

Step 2.3.1

Simplify .

Step 2.3.1.1

Rewrite.

Step 2.3.1.2

Simplify by adding zeros.

Step 2.3.1.3

Apply the distributive property.

Step 2.3.1.4

Multiply by .

Step 2.3.2

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

Step 2.3.2.1

Add to both sides of the equation.

Step 2.3.2.2

Add and .

Step 3