Enter a problem...
Calculus Examples
Step 1
Step 1.1
Differentiate using the Quotient Rule which states that is where and .
Step 1.2
Differentiate using the Exponential Rule which states that is where =.
Step 1.3
Differentiate using the Power Rule.
Step 1.3.1
Differentiate using the Power Rule which states that is where .
Step 1.3.2
Multiply by .
Step 1.4
Simplify.
Step 1.4.1
Reorder terms.
Step 1.4.2
Factor out of .
Step 1.4.2.1
Factor out of .
Step 1.4.2.2
Factor out of .
Step 1.4.2.3
Factor out of .
Step 2
Step 2.1
Differentiate using the Quotient Rule which states that is where and .
Step 2.2
Multiply the exponents in .
Step 2.2.1
Apply the power rule and multiply exponents, .
Step 2.2.2
Multiply by .
Step 2.3
Differentiate using the Product Rule which states that is where and .
Step 2.4
Differentiate.
Step 2.4.1
By the Sum Rule, the derivative of with respect to is .
Step 2.4.2
Differentiate using the Power Rule which states that is where .
Step 2.4.3
Since is constant with respect to , the derivative of with respect to is .
Step 2.4.4
Simplify the expression.
Step 2.4.4.1
Add and .
Step 2.4.4.2
Multiply by .
Step 2.5
Differentiate using the Exponential Rule which states that is where =.
Step 2.6
Differentiate using the Power Rule.
Step 2.6.1
Differentiate using the Power Rule which states that is where .
Step 2.6.2
Simplify with factoring out.
Step 2.6.2.1
Multiply by .
Step 2.6.2.2
Factor out of .
Step 2.6.2.2.1
Factor out of .
Step 2.6.2.2.2
Factor out of .
Step 2.6.2.2.3
Factor out of .
Step 2.7
Cancel the common factors.
Step 2.7.1
Factor out of .
Step 2.7.2
Cancel the common factor.
Step 2.7.3
Rewrite the expression.
Step 2.8
Simplify.
Step 2.8.1
Apply the distributive property.
Step 2.8.2
Apply the distributive property.
Step 2.8.3
Apply the distributive property.
Step 2.8.4
Simplify the numerator.
Step 2.8.4.1
Combine the opposite terms in .
Step 2.8.4.1.1
Reorder the factors in the terms and .
Step 2.8.4.1.2
Subtract from .
Step 2.8.4.1.3
Add and .
Step 2.8.4.2
Simplify each term.
Step 2.8.4.2.1
Multiply by by adding the exponents.
Step 2.8.4.2.1.1
Move .
Step 2.8.4.2.1.2
Multiply by .
Step 2.8.4.2.2
Multiply by .
Step 2.8.4.3
Reorder factors in .
Step 2.8.5
Reorder terms.
Step 2.8.6
Reorder factors in .
Step 3
The second derivative of with respect to is .