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Calculus Examples
Step 1
Step 1.1
Factor out of .
Step 1.2
Rewrite as .
Step 2
Step 2.1
Pull terms out from under the radical.
Step 2.2
By the Sum Rule, the derivative of with respect to is .
Step 3
Step 3.1
Since is constant with respect to , the derivative of with respect to is .
Step 3.2
Differentiate using the Power Rule which states that is where .
Step 3.3
Multiply by .
Step 4
Step 4.1
Use to rewrite as .
Step 4.2
Since is constant with respect to , the derivative of with respect to is .
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
Multiply the exponents in .
Step 4.6.1
Apply the power rule and multiply exponents, .
Step 4.6.2
Cancel the common factor of .
Step 4.6.2.1
Factor out of .
Step 4.6.2.2
Cancel the common factor.
Step 4.6.2.3
Rewrite the expression.
Step 4.7
To write as a fraction with a common denominator, multiply by .
Step 4.8
Combine and .
Step 4.9
Combine the numerators over the common denominator.
Step 4.10
Simplify the numerator.
Step 4.10.1
Multiply by .
Step 4.10.2
Subtract from .
Step 4.11
Move the negative in front of the fraction.
Step 4.12
Combine and .
Step 4.13
Combine and .
Step 4.14
Multiply by by adding the exponents.
Step 4.14.1
Use the power rule to combine exponents.
Step 4.14.2
To write as a fraction with a common denominator, multiply by .
Step 4.14.3
Combine and .
Step 4.14.4
Combine the numerators over the common denominator.
Step 4.14.5
Simplify the numerator.
Step 4.14.5.1
Multiply by .
Step 4.14.5.2
Subtract from .
Step 4.14.6
Move the negative in front of the fraction.
Step 4.15
Move to the denominator using the negative exponent rule .
Step 4.16
Multiply by .
Step 4.17
Combine and .
Step 4.18
Factor out of .
Step 4.19
Cancel the common factors.
Step 4.19.1
Factor out of .
Step 4.19.2
Cancel the common factor.
Step 4.19.3
Rewrite the expression.
Step 4.20
Move the negative in front of the fraction.
Step 5
Reorder terms.