Enter a problem...
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
Simplify the denominator.
Step 1.10.1.1
Rewrite as .
Step 1.10.1.2
Apply the power rule and multiply exponents, .
Step 1.10.1.3
Cancel the common factor of .
Step 1.10.1.3.1
Cancel the common factor.
Step 1.10.1.3.2
Rewrite the expression.
Step 1.10.1.4
Evaluate the exponent.
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
Cancel the common factor of .
Step 2.3.1.5.1
Factor out of .
Step 2.3.1.5.2
Factor out of .
Step 2.3.1.5.3
Cancel the common factor.
Step 2.3.1.5.4
Rewrite the expression.
Step 2.3.1.6
Combine and .
Step 2.3.1.7
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
To write as a fraction with a common denominator, multiply by .
Step 2.3.2.3
Combine and .
Step 2.3.2.4
Combine the numerators over the common denominator.
Step 2.3.2.5
Simplify the numerator.
Step 2.3.2.5.1
Multiply by .
Step 2.3.2.5.2
Add and .
Step 2.3.3
Reorder terms.
Step 3