Enter a problem...
Calculus Examples
Step 1
Use to rewrite as .
Step 2
Differentiate using the Quotient Rule which states that is where and .
Step 3
Step 3.1
Apply the power rule and multiply exponents, .
Step 3.2
Cancel the common factor of .
Step 3.2.1
Cancel the common factor.
Step 3.2.2
Rewrite the expression.
Step 4
Simplify.
Step 5
By the Sum Rule, the derivative of with respect to is .
Step 6
Differentiate using the Power Rule which states that is where .
Step 7
Since is constant with respect to , the derivative of with respect to is .
Step 8
Step 8.1
Add and .
Step 8.2
Multiply by .
Step 9
Differentiate using the Power Rule which states that is where .
Step 10
To write as a fraction with a common denominator, multiply by .
Step 11
Combine and .
Step 12
Combine the numerators over the common denominator.
Step 13
Step 13.1
Multiply by .
Step 13.2
Subtract from .
Step 14
Move the negative in front of the fraction.
Step 15
Combine and .
Step 16
Move to the denominator using the negative exponent rule .
Step 17
Step 17.1
Apply the distributive property.
Step 17.2
Apply the distributive property.
Step 17.3
Simplify the numerator.
Step 17.3.1
Simplify each term.
Step 17.3.1.1
Combine and .
Step 17.3.1.2
Move to the numerator using the negative exponent rule .
Step 17.3.1.3
Multiply by by adding the exponents.
Step 17.3.1.3.1
Multiply by .
Step 17.3.1.3.1.1
Raise to the power of .
Step 17.3.1.3.1.2
Use the power rule to combine exponents.
Step 17.3.1.3.2
Write as a fraction with a common denominator.
Step 17.3.1.3.3
Combine the numerators over the common denominator.
Step 17.3.1.3.4
Subtract from .
Step 17.3.1.4
Multiply by .
Step 17.3.1.5
Combine and .
Step 17.3.1.6
Move the negative in front of the fraction.
Step 17.3.2
To write as a fraction with a common denominator, multiply by .
Step 17.3.3
Combine and .
Step 17.3.4
Combine the numerators over the common denominator.
Step 17.3.5
Subtract from .
Step 17.3.5.1
Reorder and .
Step 17.3.5.2
Subtract from .
Step 17.4
Combine terms.
Step 17.4.1
Multiply by .
Step 17.4.2
Combine.
Step 17.4.3
Apply the distributive property.
Step 17.4.4
Cancel the common factor of .
Step 17.4.4.1
Cancel the common factor.
Step 17.4.4.2
Rewrite the expression.
Step 17.4.5
Multiply by .
Step 17.4.6
Combine and .
Step 17.4.7
Multiply by .
Step 17.4.8
Factor out of .
Step 17.4.9
Cancel the common factors.
Step 17.4.9.1
Factor out of .
Step 17.4.9.2
Cancel the common factor.
Step 17.4.9.3
Rewrite the expression.
Step 17.4.10
Move the negative in front of the fraction.
Step 17.5
Simplify the numerator.
Step 17.5.1
To write as a fraction with a common denominator, multiply by .
Step 17.5.2
Combine the numerators over the common denominator.
Step 17.5.3
Simplify the numerator.
Step 17.5.3.1
Multiply by by adding the exponents.
Step 17.5.3.1.1
Use the power rule to combine exponents.
Step 17.5.3.1.2
Combine the numerators over the common denominator.
Step 17.5.3.1.3
Add and .
Step 17.5.3.1.4
Divide by .
Step 17.5.3.2
Simplify .
Step 17.6
Multiply the numerator by the reciprocal of the denominator.
Step 17.7
Multiply .
Step 17.7.1
Multiply by .
Step 17.7.2
Multiply by by adding the exponents.
Step 17.7.2.1
Move .
Step 17.7.2.2
Multiply by .
Step 17.7.2.2.1
Raise to the power of .
Step 17.7.2.2.2
Use the power rule to combine exponents.
Step 17.7.2.3
Write as a fraction with a common denominator.
Step 17.7.2.4
Combine the numerators over the common denominator.
Step 17.7.2.5
Add and .
Step 17.8
Move to the left of .