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Calculus Examples
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Step 1
Step 1.1
Since is constant with respect to , the derivative of with respect to is .
Step 1.2
Rewrite as .
Step 1.3
Differentiate using the Power Rule which states that is where .
Step 1.4
Multiply by .
Step 1.5
Simplify.
Step 1.5.1
Rewrite the expression using the negative exponent rule .
Step 1.5.2
Combine terms.
Step 1.5.2.1
Combine and .
Step 1.5.2.2
Move the negative in front of the fraction.
Step 1.6
Evaluate the derivative at .
Step 1.7
Raise to the power of .
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 terms.
Step 2.3.1.2.1
Apply the distributive property.
Step 2.3.1.2.2
Combine and .
Step 2.3.1.2.3
Cancel the common factor of .
Step 2.3.1.2.3.1
Move the leading negative in into the numerator.
Step 2.3.1.2.3.2
Factor out of .
Step 2.3.1.2.3.3
Factor out of .
Step 2.3.1.2.3.4
Cancel the common factor.
Step 2.3.1.2.3.5
Rewrite the expression.
Step 2.3.1.2.4
Combine and .
Step 2.3.1.2.5
Multiply by .
Step 2.3.1.3
Move to the left of .
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
Combine the numerators over the common denominator.
Step 2.3.2.3
Add and .
Step 2.3.2.4
Move the negative in front of the fraction.
Step 2.3.3
Write in form.
Step 2.3.3.1
Reorder terms.
Step 2.3.3.2
Remove parentheses.
Step 3