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Calculus Examples
Step 1
Differentiate using the Quotient Rule which states that is where and .
Step 2
Step 2.1
Apply the power rule and multiply exponents, .
Step 2.2
Move to the left of .
Step 3
The derivative of with respect to is .
Step 4
Combine and .
Step 5
Multiply by .
Step 6
Step 6.1
Combine.
Step 6.2
Apply the distributive property.
Step 6.3
Cancel the common factor of .
Step 6.3.1
Cancel the common factor.
Step 6.3.2
Rewrite the expression.
Step 7
Differentiate using the Exponential Rule which states that is where =.
Step 8
Step 8.1
Rewrite using the commutative property of multiplication.
Step 8.2
Reorder terms.
Step 8.3
Factor out of .
Step 8.3.1
Factor out of .
Step 8.3.2
Multiply by .
Step 8.3.3
Factor out of .
Step 8.4
Cancel the common factor of and .
Step 8.4.1
Factor out of .
Step 8.4.2
Cancel the common factors.
Step 8.4.2.1
Factor out of .
Step 8.4.2.2
Cancel the common factor.
Step 8.4.2.3
Rewrite the expression.
Step 8.5
Factor out of .
Step 8.6
Rewrite as .
Step 8.7
Factor out of .
Step 8.8
Rewrite as .
Step 8.9
Move the negative in front of the fraction.