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Calculus Examples
Step 1
Differentiate both sides of the equation.
Step 2
The derivative of with respect to is .
Step 3
Step 3.1
Apply basic rules of exponents.
Step 3.1.1
Rewrite as .
Step 3.1.2
Multiply the exponents in .
Step 3.1.2.1
Apply the power rule and multiply exponents, .
Step 3.1.2.2
Move to the left of .
Step 3.1.2.3
Rewrite as .
Step 3.2
Differentiate using the chain rule, which states that is where and .
Step 3.2.1
To apply the Chain Rule, set as .
Step 3.2.2
Differentiate using the Exponential Rule which states that is where =.
Step 3.2.3
Replace all occurrences of with .
Step 3.3
Differentiate.
Step 3.3.1
Since is constant with respect to , the derivative of with respect to is .
Step 3.3.2
Differentiate using the Power Rule which states that is where .
Step 3.3.3
Simplify the expression.
Step 3.3.3.1
Multiply by .
Step 3.3.3.2
Move to the left of .
Step 3.3.3.3
Rewrite as .
Step 4
Reform the equation by setting the left side equal to the right side.
Step 5
Replace with .