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Calculus Examples
Step 1
Use to rewrite as .
Step 2
Step 2.1
To apply the Chain Rule, set as .
Step 2.2
The derivative of with respect to is .
Step 2.3
Replace all occurrences of with .
Step 3
Step 3.1
By the Sum Rule, the derivative of with respect to is .
Step 3.2
Differentiate using the Power Rule which states that is where .
Step 4
Step 4.1
To apply the Chain Rule, set as .
Step 4.2
Differentiate using the Power Rule which states that is where .
Step 4.3
Replace all occurrences of with .
Step 5
To write as a fraction with a common denominator, multiply by .
Step 6
Combine and .
Step 7
Combine the numerators over the common denominator.
Step 8
Step 8.1
Multiply by .
Step 8.2
Subtract from .
Step 9
Step 9.1
Move the negative in front of the fraction.
Step 9.2
Combine and .
Step 9.3
Move to the denominator using the negative exponent rule .
Step 10
By the Sum Rule, the derivative of with respect to is .
Step 11
Since is constant with respect to , the derivative of with respect to is .
Step 12
Add and .
Step 13
Differentiate using the Power Rule which states that is where .
Step 14
Step 14.1
Combine and .
Step 14.2
Combine and .
Step 14.3
Cancel the common factor.
Step 14.4
Rewrite the expression.
Step 15
Step 15.1
Reorder the factors of .
Step 15.2
Multiply by .
Step 15.3
Multiply the numerator and denominator of the fraction by .
Step 15.3.1
Multiply by .
Step 15.3.2
Combine.
Step 15.4
Apply the distributive property.
Step 15.5
Cancel the common factor of .
Step 15.5.1
Cancel the common factor.
Step 15.5.2
Rewrite the expression.
Step 15.6
Multiply by .
Step 15.7
Simplify the denominator.
Step 15.7.1
Multiply by by adding the exponents.
Step 15.7.1.1
Use the power rule to combine exponents.
Step 15.7.1.2
Combine the numerators over the common denominator.
Step 15.7.1.3
Add and .
Step 15.7.1.4
Divide by .
Step 15.7.2
Simplify .
Step 15.7.3
Reorder terms.