Enter a problem...
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
Differentiate using the Product Rule which states that is where and .
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 9.4
Combine and .
Step 10
By the Sum Rule, the derivative of with respect to is .
Step 11
Differentiate using the Power Rule which states that is where .
Step 12
Since is constant with respect to , the derivative of with respect to is .
Step 13
Step 13.1
Add and .
Step 13.2
Combine and .
Step 13.3
Combine and .
Step 14
Raise to the power of .
Step 15
Raise to the power of .
Step 16
Use the power rule to combine exponents.
Step 17
Step 17.1
Add and .
Step 17.2
Cancel the common factor.
Step 17.3
Rewrite the expression.
Step 18
Differentiate using the Power Rule which states that is where .
Step 19
Multiply by .
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
Add and .
Step 25
Multiply by .
Step 26
Step 26.1
Move .
Step 26.2
Use the power rule to combine exponents.
Step 26.3
Combine the numerators over the common denominator.
Step 26.4
Add and .
Step 26.5
Divide by .
Step 27
Simplify .
Step 28
Step 28.1
Apply the distributive property.
Step 28.2
Combine terms.
Step 28.2.1
Multiply by by adding the exponents.
Step 28.2.1.1
Multiply by .
Step 28.2.1.1.1
Raise to the power of .
Step 28.2.1.1.2
Use the power rule to combine exponents.
Step 28.2.1.2
Add and .
Step 28.2.2
Move to the left of .
Step 28.2.3
Rewrite as .