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Calculus Examples
Step 1
Use to rewrite as .
Step 2
Differentiate using the Quotient Rule which states that is where and .
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
Step 5.1
Differentiate using the Power Rule which states that is where .
Step 5.2
Multiply by .
Step 6
Step 6.1
To apply the Chain Rule, set as .
Step 6.2
Differentiate using the Power Rule which states that is where .
Step 6.3
Replace all occurrences of with .
Step 7
To write as a fraction with a common denominator, multiply by .
Step 8
Combine and .
Step 9
Combine the numerators over the common denominator.
Step 10
Step 10.1
Multiply by .
Step 10.2
Subtract from .
Step 11
Step 11.1
Move the negative in front of the fraction.
Step 11.2
Combine and .
Step 11.3
Move to the denominator using the negative exponent rule .
Step 11.4
Combine and .
Step 12
By the Sum Rule, the derivative of with respect to is .
Step 13
Since is constant with respect to , the derivative of with respect to is .
Step 14
Differentiate using the Power Rule which states that is where .
Step 15
Multiply by .
Step 16
Since is constant with respect to , the derivative of with respect to is .
Step 17
Step 17.1
Add and .
Step 17.2
Multiply by .
Step 17.3
Combine and .
Step 17.4
Factor out of .
Step 18
Step 18.1
Factor out of .
Step 18.2
Cancel the common factor.
Step 18.3
Rewrite the expression.
Step 19
Move the negative in front of the fraction.
Step 20
To write as a fraction with a common denominator, multiply by .
Step 21
Combine the numerators over the common denominator.
Step 22
Step 22.1
Use the power rule to combine exponents.
Step 22.2
Combine the numerators over the common denominator.
Step 22.3
Add and .
Step 22.4
Divide by .
Step 23
Simplify .
Step 24
Subtract from .
Step 25
Rewrite as a product.
Step 26
Multiply by .
Step 27
Step 27.1
Multiply by .
Step 27.1.1
Raise to the power of .
Step 27.1.2
Use the power rule to combine exponents.
Step 27.2
Write as a fraction with a common denominator.
Step 27.3
Combine the numerators over the common denominator.
Step 27.4
Add and .