Enter a problem...
Calculus Examples
at
Step 1
Step 1.1
Simplify with factoring out.
Step 1.1.1
Use to rewrite as .
Step 1.1.2
Factor out of .
Step 1.1.3
Apply the product rule to .
Step 1.2
Since is constant with respect to , the derivative of with respect to is .
Step 1.3
Differentiate using the Power Rule which states that is where .
Step 1.4
To write as a fraction with a common denominator, multiply by .
Step 1.5
Combine and .
Step 1.6
Combine the numerators over the common denominator.
Step 1.7
Simplify the numerator.
Step 1.7.1
Multiply by .
Step 1.7.2
Subtract from .
Step 1.8
Move the negative in front of the fraction.
Step 1.9
Combine and .
Step 1.10
Combine and .
Step 1.11
Simplify the expression.
Step 1.11.1
Move to the denominator using the negative exponent rule .
Step 1.11.2
Move to the denominator using the negative exponent rule .
Step 1.12
Multiply by by adding the exponents.
Step 1.12.1
Multiply by .
Step 1.12.1.1
Raise to the power of .
Step 1.12.1.2
Use the power rule to combine exponents.
Step 1.12.2
Write as a fraction with a common denominator.
Step 1.12.3
Combine the numerators over the common denominator.
Step 1.12.4
Subtract from .
Step 1.13
Evaluate the derivative at .
Step 1.14
Simplify.
Step 1.14.1
Multiply by by adding the exponents.
Step 1.14.1.1
Use the power rule to combine exponents.
Step 1.14.1.2
Combine the numerators over the common denominator.
Step 1.14.1.3
Add and .
Step 1.14.1.4
Divide by .
Step 1.14.2
Simplify .
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
Cancel the common factor.
Step 2.3.1.5.3
Rewrite the expression.
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 2.3.3
Reorder terms.
Step 3