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Calculus Examples
Step 1
Since is constant with respect to , the derivative of with respect to is .
Step 2
Differentiate using the Quotient Rule which states that is where and .
Step 3
The derivative of with respect to is .
Step 4
Step 4.1
By the Sum Rule, the derivative of with respect to is .
Step 4.2
Since is constant with respect to , the derivative of with respect to is .
Step 4.3
Differentiate using the Power Rule which states that is where .
Step 4.4
Multiply by .
Step 4.5
Since is constant with respect to , the derivative of with respect to is .
Step 4.6
Differentiate using the Power Rule which states that is where .
Step 4.7
Combine fractions.
Step 4.7.1
Multiply by .
Step 4.7.2
Combine and .
Step 5
Step 5.1
Apply the distributive property.
Step 5.2
Apply the distributive property.
Step 5.3
Apply the distributive property.
Step 5.4
Simplify the numerator.
Step 5.4.1
Simplify each term.
Step 5.4.1.1
Cancel the common factor of .
Step 5.4.1.1.1
Factor out of .
Step 5.4.1.1.2
Cancel the common factor.
Step 5.4.1.1.3
Rewrite the expression.
Step 5.4.1.2
Cancel the common factor of .
Step 5.4.1.2.1
Factor out of .
Step 5.4.1.2.2
Cancel the common factor.
Step 5.4.1.2.3
Rewrite the expression.
Step 5.4.1.3
Multiply by .
Step 5.4.1.4
Multiply .
Step 5.4.1.4.1
Multiply by .
Step 5.4.1.4.2
Reorder and .
Step 5.4.1.4.3
Simplify by moving inside the logarithm.
Step 5.4.1.5
Multiply .
Step 5.4.1.5.1
Multiply by .
Step 5.4.1.5.2
Simplify by moving inside the logarithm.
Step 5.4.1.6
Multiply .
Step 5.4.1.6.1
Reorder and .
Step 5.4.1.6.2
Simplify by moving inside the logarithm.
Step 5.4.1.7
Multiply the exponents in .
Step 5.4.1.7.1
Apply the power rule and multiply exponents, .
Step 5.4.1.7.2
Multiply by .
Step 5.4.2
Reorder factors in .
Step 5.5
Reorder terms.
Step 5.6
Simplify the denominator.
Step 5.6.1
Factor out of .
Step 5.6.1.1
Factor out of .
Step 5.6.1.2
Factor out of .
Step 5.6.1.3
Factor out of .
Step 5.6.2
Apply the product rule to .