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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
Differentiate using the Power Rule which states that is where .
Step 2.3
Replace all occurrences of with .
Step 3
To write as a fraction with a common denominator, multiply by .
Step 4
Combine and .
Step 5
Combine the numerators over the common denominator.
Step 6
Step 6.1
Multiply by .
Step 6.2
Subtract from .
Step 7
Step 7.1
Move the negative in front of the fraction.
Step 7.2
Combine and .
Step 7.3
Move to the denominator using the negative exponent rule .
Step 8
Differentiate using the Product Rule which states that is where and .
Step 9
Step 9.1
To apply the Chain Rule, set as .
Step 9.2
The derivative of with respect to is .
Step 9.3
Replace all occurrences of with .
Step 10
Step 10.1
Combine and .
Step 10.2
Cancel the common factor of and .
Step 10.2.1
Raise to the power of .
Step 10.2.2
Factor out of .
Step 10.2.3
Cancel the common factors.
Step 10.2.3.1
Factor out of .
Step 10.2.3.2
Cancel the common factor.
Step 10.2.3.3
Rewrite the expression.
Step 10.3
Differentiate using the Power Rule which states that is where .
Step 10.4
Simplify terms.
Step 10.4.1
Combine and .
Step 10.4.2
Combine and .
Step 10.4.3
Cancel the common factor of .
Step 10.4.3.1
Cancel the common factor.
Step 10.4.3.2
Divide by .
Step 10.5
Differentiate using the Power Rule which states that is where .
Step 10.6
Multiply by .
Step 11
Step 11.1
Apply the product rule to .
Step 11.2
Apply the distributive property.
Step 11.3
Combine terms.
Step 11.3.1
Combine and .
Step 11.3.2
Factor out of .
Step 11.3.3
Cancel the common factors.
Step 11.3.3.1
Factor out of .
Step 11.3.3.2
Cancel the common factor.
Step 11.3.3.3
Rewrite the expression.
Step 11.3.4
Combine and .
Step 11.3.5
Move to the numerator using the negative exponent rule .
Step 11.3.6
Multiply by by adding the exponents.
Step 11.3.6.1
Multiply by .
Step 11.3.6.1.1
Raise to the power of .
Step 11.3.6.1.2
Use the power rule to combine exponents.
Step 11.3.6.2
Write as a fraction with a common denominator.
Step 11.3.6.3
Combine the numerators over the common denominator.
Step 11.3.6.4
Subtract from .