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Calculus Examples
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Step 1
Step 1.1
Differentiate both sides of the equation.
Step 1.2
Differentiate the left side of the equation.
Step 1.2.1
Differentiate.
Step 1.2.1.1
By the Sum Rule, the derivative of with respect to is .
Step 1.2.1.2
Differentiate using the Power Rule which states that is where .
Step 1.2.2
Evaluate .
Step 1.2.2.1
Differentiate using the chain rule, which states that is where and .
Step 1.2.2.1.1
To apply the Chain Rule, set as .
Step 1.2.2.1.2
Differentiate using the Power Rule which states that is where .
Step 1.2.2.1.3
Replace all occurrences of with .
Step 1.2.2.2
Rewrite as .
Step 1.2.3
Reorder terms.
Step 1.3
Since is constant with respect to , the derivative of with respect to is .
Step 1.4
Reform the equation by setting the left side equal to the right side.
Step 1.5
Solve for .
Step 1.5.1
Subtract from both sides of the equation.
Step 1.5.2
Divide each term in by and simplify.
Step 1.5.2.1
Divide each term in by .
Step 1.5.2.2
Simplify the left side.
Step 1.5.2.2.1
Cancel the common factor of .
Step 1.5.2.2.1.1
Cancel the common factor.
Step 1.5.2.2.1.2
Rewrite the expression.
Step 1.5.2.2.2
Cancel the common factor of .
Step 1.5.2.2.2.1
Cancel the common factor.
Step 1.5.2.2.2.2
Divide by .
Step 1.5.2.3
Simplify the right side.
Step 1.5.2.3.1
Cancel the common factor of and .
Step 1.5.2.3.1.1
Factor out of .
Step 1.5.2.3.1.2
Cancel the common factors.
Step 1.5.2.3.1.2.1
Factor out of .
Step 1.5.2.3.1.2.2
Cancel the common factor.
Step 1.5.2.3.1.2.3
Rewrite the expression.
Step 1.5.2.3.2
Move the negative in front of the fraction.
Step 1.6
Replace with .
Step 1.7
Evaluate at and .
Step 1.7.1
Replace the variable with in the expression.
Step 1.7.2
Replace the variable with in the expression.
Step 1.7.3
Divide by .
Step 1.7.4
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
Add and .
Step 2.3.1.2
Multiply by .
Step 2.3.2
Add to both sides of the equation.
Step 3