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Calculus Examples
Step 1
Step 1.1
To apply the Chain Rule, set as .
Step 1.2
The derivative of with respect to is .
Step 1.3
Replace all occurrences of with .
Step 2
Differentiate using the Quotient Rule which states that is where and .
Step 3
Step 3.1
By the Sum Rule, the derivative of with respect to is .
Step 3.2
Since is constant with respect to , the derivative of with respect to is .
Step 3.3
Add and .
Step 3.4
Since is constant with respect to , the derivative of with respect to is .
Step 4
Step 4.1
To apply the Chain Rule, set as .
Step 4.2
Differentiate using the Exponential Rule which states that is where =.
Step 4.3
Replace all occurrences of with .
Step 5
Step 5.1
Since is constant with respect to , the derivative of with respect to is .
Step 5.2
Multiply by .
Step 5.3
Differentiate using the Power Rule which states that is where .
Step 5.4
Multiply by .
Step 5.5
By the Sum Rule, the derivative of with respect to is .
Step 5.6
Since is constant with respect to , the derivative of with respect to is .
Step 5.7
Add and .
Step 6
Step 6.1
To apply the Chain Rule, set as .
Step 6.2
Differentiate using the Exponential Rule which states that is where =.
Step 6.3
Replace all occurrences of with .
Step 7
Step 7.1
Since is constant with respect to , the derivative of with respect to is .
Step 7.2
Multiply by .
Step 7.3
Differentiate using the Power Rule which states that is where .
Step 7.4
Combine fractions.
Step 7.4.1
Multiply by .
Step 7.4.2
Combine and .
Step 8
Step 8.1
Apply the distributive property.
Step 8.2
Apply the distributive property.
Step 8.3
Apply the distributive property.
Step 8.4
Simplify the numerator.
Step 8.4.1
Simplify each term.
Step 8.4.1.1
Multiply by .
Step 8.4.1.2
Rewrite using the commutative property of multiplication.
Step 8.4.1.3
Multiply by by adding the exponents.
Step 8.4.1.3.1
Move .
Step 8.4.1.3.2
Use the power rule to combine exponents.
Step 8.4.1.3.3
Add and .
Step 8.4.1.4
Multiply by .
Step 8.4.1.5
Multiply by by adding the exponents.
Step 8.4.1.5.1
Move .
Step 8.4.1.5.2
Use the power rule to combine exponents.
Step 8.4.1.5.3
Add and .
Step 8.4.1.6
Multiply by .
Step 8.4.2
Combine the opposite terms in .
Step 8.4.2.1
Add and .
Step 8.4.2.2
Add and .
Step 8.4.3
Subtract from .
Step 8.5
Combine terms.
Step 8.5.1
Move the negative in front of the fraction.
Step 8.5.2
Multiply by .
Step 8.5.3
Multiply by .