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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
Apply the power rule and multiply exponents, .
Step 3.2
Cancel the common factor of .
Step 3.2.1
Cancel the common factor.
Step 3.2.2
Rewrite the expression.
Step 4
Simplify.
Step 5
Write as a fraction with a common denominator.
Step 6
Combine the numerators over the common denominator.
Step 7
Add and .
Step 8
Add and .
Step 9
Add and .
Step 10
Multiply by the reciprocal of the fraction to divide by .
Step 11
Multiply by .
Step 12
Step 12.1
To apply the Chain Rule, set as .
Step 12.2
Differentiate using the Power Rule which states that is where .
Step 12.3
Replace all occurrences of with .
Step 13
To write as a fraction with a common denominator, multiply by .
Step 14
Combine and .
Step 15
Combine the numerators over the common denominator.
Step 16
Step 16.1
Multiply by .
Step 16.2
Subtract from .
Step 17
Step 17.1
Move the negative in front of the fraction.
Step 17.2
Multiply by .
Step 17.3
Multiply by .
Step 18
Differentiate using the Quotient Rule which states that is where and .
Step 19
Step 19.1
By the Sum Rule, the derivative of with respect to is .
Step 19.2
Since is constant with respect to , the derivative of with respect to is .
Step 19.3
Add and .
Step 19.4
Differentiate using the Power Rule which states that is where .
Step 19.5
Multiply by .
Step 19.6
By the Sum Rule, the derivative of with respect to is .
Step 19.7
Since is constant with respect to , the derivative of with respect to is .
Step 19.8
Add and .
Step 19.9
Since is constant with respect to , the derivative of with respect to is .
Step 19.10
Multiply.
Step 19.10.1
Multiply by .
Step 19.10.2
Multiply by .
Step 19.11
Differentiate using the Power Rule which states that is where .
Step 19.12
Simplify terms.
Step 19.12.1
Multiply by .
Step 19.12.2
Add and .
Step 19.12.3
Add and .
Step 19.12.4
Add and .
Step 19.12.5
Multiply by .
Step 19.12.6
Move to the left of .
Step 20
Step 20.1
Factor out of .
Step 20.2
Cancel the common factor.
Step 20.3
Rewrite the expression.
Step 21
Step 21.1
Multiply by .
Step 21.2
Cancel the common factors.
Step 21.2.1
Factor out of .
Step 21.2.2
Cancel the common factor.
Step 21.2.3
Rewrite the expression.
Step 22
Step 22.1
Change the sign of the exponent by rewriting the base as its reciprocal.
Step 22.2
Apply the product rule to .
Step 22.3
Apply the distributive property.
Step 22.4
Combine terms.
Step 22.4.1
Multiply by .
Step 22.4.2
Multiply by .
Step 22.4.3
Multiply by .
Step 22.5
Reorder terms.
Step 22.6
Factor out of .
Step 22.6.1
Factor out of .
Step 22.6.2
Factor out of .
Step 22.6.3
Factor out of .
Step 22.7
Reorder terms.
Step 22.8
Factor out of .
Step 22.9
Cancel the common factors.
Step 22.9.1
Factor out of .
Step 22.9.2
Cancel the common factor.
Step 22.9.3
Rewrite the expression.
Step 22.10
Move to the denominator using the negative exponent rule .
Step 22.11
Move to the left of .