Enter a problem...
Calculus Examples
Step 1
Step 1.1
Let . Find .
Step 1.1.1
Differentiate .
Step 1.1.2
Differentiate.
Step 1.1.2.1
By the Sum Rule, the derivative of with respect to is .
Step 1.1.2.2
Since is constant with respect to , the derivative of with respect to is .
Step 1.1.3
Evaluate .
Step 1.1.3.1
Differentiate using the chain rule, which states that is where and .
Step 1.1.3.1.1
To apply the Chain Rule, set as .
Step 1.1.3.1.2
Differentiate using the Exponential Rule which states that is where =.
Step 1.1.3.1.3
Replace all occurrences of with .
Step 1.1.3.2
Since is constant with respect to , the derivative of with respect to is .
Step 1.1.3.3
Differentiate using the Power Rule which states that is where .
Step 1.1.3.4
Multiply by .
Step 1.1.3.5
Move to the left of .
Step 1.1.4
Add and .
Step 1.2
Rewrite the problem using and .
Step 2
Step 2.1
Multiply by .
Step 2.2
Move to the left of .
Step 3
Since is constant with respect to , move out of the integral.
Step 4
The integral of with respect to is .
Step 5
Simplify.
Step 6
Replace all occurrences of with .