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Calculus Examples
,
Step 1
Step 1.1
Use to rewrite as .
Step 1.2
Differentiate using the Power Rule which states that is where .
Step 1.3
To write as a fraction with a common denominator, multiply by .
Step 1.4
Combine and .
Step 1.5
Combine the numerators over the common denominator.
Step 1.6
Simplify the numerator.
Step 1.6.1
Multiply by .
Step 1.6.2
Subtract from .
Step 1.7
Move the negative in front of the fraction.
Step 1.8
Simplify.
Step 1.8.1
Rewrite the expression using the negative exponent rule .
Step 1.8.2
Multiply by .
Step 1.9
Evaluate the derivative at .
Step 1.10
Simplify.
Step 1.10.1
One to any power is one.
Step 1.10.2
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
Combine and .
Step 2.3.1.5
Combine and .
Step 2.3.1.6
Move the negative in front of the fraction.
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
Write as a fraction with a common denominator.
Step 2.3.2.3
Combine the numerators over the common denominator.
Step 2.3.2.4
Add and .
Step 2.3.3
Reorder terms.
Step 3