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Calculus Examples
Step 1
By the Sum Rule, the derivative of with respect to is .
Step 2
Step 2.1
Differentiate using the Product Rule which states that is where and .
Step 2.2
Differentiate using the chain rule, which states that is where and .
Step 2.2.1
To apply the Chain Rule, set as .
Step 2.2.2
The derivative of with respect to is .
Step 2.2.3
Replace all occurrences of with .
Step 2.3
Since is constant with respect to , the derivative of with respect to is .
Step 2.4
Differentiate using the Power Rule which states that is where .
Step 2.5
Differentiate using the Power Rule which states that is where .
Step 2.6
Factor out of .
Step 2.7
Apply the product rule to .
Step 2.8
Raise to the power of .
Step 2.9
Multiply by .
Step 2.10
Combine and .
Step 2.11
Combine and .
Step 2.12
Move to the left of .
Step 2.13
Multiply by .
Step 2.14
To write as a fraction with a common denominator, multiply by .
Step 2.15
Combine the numerators over the common denominator.
Step 3
Step 3.1
Since is constant with respect to , the derivative of with respect to is .
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
The derivative of with respect to is .
Step 3.2.3
Replace all occurrences of with .
Step 3.3
By the Sum Rule, the derivative of with respect to is .
Step 3.4
Since is constant with respect to , the derivative of with respect to is .
Step 3.5
Since is constant with respect to , the derivative of with respect to is .
Step 3.6
Differentiate using the Power Rule which states that is where .
Step 3.7
Multiply by .
Step 3.8
Add and .
Step 3.9
Combine and .
Step 3.10
Combine and .
Step 3.11
Multiply by .
Step 3.12
Move to the left of .
Step 3.13
Cancel the common factor of and .
Step 3.13.1
Factor out of .
Step 3.13.2
Cancel the common factors.
Step 3.13.2.1
Cancel the common factor.
Step 3.13.2.2
Rewrite the expression.
Step 4
Step 4.1
Apply the distributive property.
Step 4.2
Combine terms.
Step 4.2.1
Multiply by .
Step 4.2.2
Combine the numerators over the common denominator.
Step 4.2.3
Subtract from .
Step 4.2.4
Add and .
Step 4.3
Reorder terms.
Step 4.4
Factor out of .
Step 4.4.1
Factor out of .
Step 4.4.2
Multiply by .
Step 4.4.3
Factor out of .
Step 4.5
Cancel the common factor of .
Step 4.5.1
Cancel the common factor.
Step 4.5.2
Divide by .