Calculus Examples

Find the Derivative - d/d@VAR f(x)=(11x^2-22x+22)e^x
Step 1
Differentiate using the Product Rule which states that is where and .
Step 2
Differentiate using the Exponential Rule which states that is where =.
Step 3
Differentiate.
Tap for more steps...
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
Differentiate using the Power Rule which states that is where .
Step 3.4
Multiply by .
Step 3.5
Since is constant with respect to , the derivative of with respect to is .
Step 3.6
Differentiate using the Power Rule which states that is where .
Step 3.7
Multiply by .
Step 3.8
Since is constant with respect to , the derivative of with respect to is .
Step 3.9
Add and .
Step 4
Simplify.
Tap for more steps...
Step 4.1
Apply the distributive property.
Step 4.2
Apply the distributive property.
Step 4.3
Combine terms.
Tap for more steps...
Step 4.3.1
Move to the left of .
Step 4.3.2
Add and .
Tap for more steps...
Step 4.3.2.1
Move .
Step 4.3.2.2
Add and .
Step 4.3.3
Add and .
Step 4.3.4
Subtract from .
Step 4.3.5
Add and .
Step 4.4
Reorder the factors of .
Step 4.5
Reorder factors in .