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Calculus Examples
Step 1
Step 1.1
Use to rewrite as .
Step 1.2
Factor out of .
Step 1.3
Apply the product rule to .
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
Since is constant with respect to , the derivative of with respect to is .
Step 3.2
Combine and .
Step 3.3
Differentiate using the Power Rule which states that is where .
Step 4
To write as a fraction with a common denominator, multiply by .
Step 5
Combine and .
Step 6
Combine the numerators over the common denominator.
Step 7
Step 7.1
Multiply by .
Step 7.2
Subtract from .
Step 8
Move the negative in front of the fraction.
Step 9
Combine and .
Step 10
Multiply by .
Step 11
Step 11.1
Move to the left of .
Step 11.2
Move to the denominator using the negative exponent rule .
Step 12
Step 12.1
Apply the product rule to .
Step 12.2
Apply the distributive property.
Step 12.3
Apply the distributive property.
Step 12.4
Combine terms.
Step 12.4.1
Multiply by .
Step 12.4.2
Multiply the exponents in .
Step 12.4.2.1
Apply the power rule and multiply exponents, .
Step 12.4.2.2
Cancel the common factor of .
Step 12.4.2.2.1
Cancel the common factor.
Step 12.4.2.2.2
Rewrite the expression.
Step 12.4.3
Evaluate the exponent.
Step 12.4.4
Multiply the exponents in .
Step 12.4.4.1
Apply the power rule and multiply exponents, .
Step 12.4.4.2
Cancel the common factor of .
Step 12.4.4.2.1
Cancel the common factor.
Step 12.4.4.2.2
Rewrite the expression.
Step 12.4.5
Simplify.
Step 12.4.6
Multiply by .
Step 12.4.7
Multiply by by adding the exponents.
Step 12.4.7.1
Move .
Step 12.4.7.2
Multiply by .
Step 12.4.7.2.1
Raise to the power of .
Step 12.4.7.2.2
Use the power rule to combine exponents.
Step 12.4.7.3
Write as a fraction with a common denominator.
Step 12.4.7.4
Combine the numerators over the common denominator.
Step 12.4.7.5
Add and .
Step 12.5
Reorder terms.
Step 12.6
Simplify the denominator.
Step 12.6.1
Factor out of .
Step 12.6.1.1
Factor out of .
Step 12.6.1.2
Factor out of .
Step 12.6.1.3
Factor out of .
Step 12.6.2
Divide by .
Step 12.6.3
Simplify.