Enter a problem...
Calculus Examples
Step 1
By the Sum Rule, the derivative of with respect to is .
Step 2
Step 2.1
Rewrite as .
Step 2.2
Differentiate using the Power Rule which states that is where .
Step 3
Step 3.1
Rewrite as .
Step 3.2
Differentiate using the chain rule, which states that is where and .
Step 3.2.1
To apply the Chain Rule, set as .
Step 3.2.2
Differentiate using the Power Rule which states that is where .
Step 3.2.3
Replace all occurrences of with .
Step 3.3
Differentiate using the Power Rule which states that is where .
Step 3.4
Multiply the exponents in .
Step 3.4.1
Apply the power rule and multiply exponents, .
Step 3.4.2
Multiply by .
Step 3.5
Multiply by .
Step 3.6
Raise to the power of .
Step 3.7
Use the power rule to combine exponents.
Step 3.8
Subtract from .
Step 4
Step 4.1
Use to rewrite as .
Step 4.2
Differentiate using the Product Rule which states that is where and .
Step 4.3
Rewrite as .
Step 4.4
Differentiate using the chain rule, which states that is where and .
Step 4.4.1
To apply the Chain Rule, set as .
Step 4.4.2
Differentiate using the Power Rule which states that is where .
Step 4.4.3
Replace all occurrences of with .
Step 4.5
Differentiate using the Power Rule which states that is where .
Step 4.6
Since is constant with respect to , the derivative of with respect to is .
Step 4.7
Multiply the exponents in .
Step 4.7.1
Apply the power rule and multiply exponents, .
Step 4.7.2
Cancel the common factor of .
Step 4.7.2.1
Factor out of .
Step 4.7.2.2
Cancel the common factor.
Step 4.7.2.3
Rewrite the expression.
Step 4.8
To write as a fraction with a common denominator, multiply by .
Step 4.9
Combine and .
Step 4.10
Combine the numerators over the common denominator.
Step 4.11
Simplify the numerator.
Step 4.11.1
Multiply by .
Step 4.11.2
Subtract from .
Step 4.12
Move the negative in front of the fraction.
Step 4.13
Combine and .
Step 4.14
Combine and .
Step 4.15
Multiply by by adding the exponents.
Step 4.15.1
Use the power rule to combine exponents.
Step 4.15.2
To write as a fraction with a common denominator, multiply by .
Step 4.15.3
Combine and .
Step 4.15.4
Combine the numerators over the common denominator.
Step 4.15.5
Simplify the numerator.
Step 4.15.5.1
Multiply by .
Step 4.15.5.2
Subtract from .
Step 4.15.6
Move the negative in front of the fraction.
Step 4.16
Move to the denominator using the negative exponent rule .
Step 4.17
Multiply by .
Step 4.18
Multiply by .
Step 4.19
Multiply by .
Step 4.20
Add and .
Step 5
Rewrite the expression using the negative exponent rule .
Step 6
Rewrite the expression using the negative exponent rule .
Step 7
Step 7.1
Combine and .
Step 7.2
Move the negative in front of the fraction.