Calculus Examples

Find dy/dx y=(x^2-3x+3)e^((5x)/3)
Step 1
Differentiate both sides of the equation.
Step 2
The derivative of with respect to is .
Step 3
Differentiate the right side of the equation.
Tap for more steps...
Step 3.1
Differentiate using the Product Rule which states that is where and .
Step 3.2
Differentiate using the chain rule, which states that is where and .
Tap for more steps...
Step 3.2.1
To apply the Chain Rule, set as .
Step 3.2.2
Differentiate using the Exponential Rule which states that is where =.
Step 3.2.3
Replace all occurrences of with .
Step 3.3
Differentiate.
Tap for more steps...
Step 3.3.1
Since is constant with respect to , the derivative of with respect to is .
Step 3.3.2
Combine and .
Step 3.3.3
Differentiate using the Power Rule which states that is where .
Step 3.3.4
Multiply by .
Step 3.3.5
By the Sum Rule, the derivative of with respect to is .
Step 3.3.6
Differentiate using the Power Rule which states that is where .
Step 3.3.7
Since is constant with respect to , the derivative of with respect to is .
Step 3.3.8
Differentiate using the Power Rule which states that is where .
Step 3.3.9
Multiply by .
Step 3.3.10
Since is constant with respect to , the derivative of with respect to is .
Step 3.3.11
Add and .
Step 3.4
Simplify.
Tap for more steps...
Step 3.4.1
Apply the distributive property.
Step 3.4.2
Apply the distributive property.
Step 3.4.3
Combine terms.
Tap for more steps...
Step 3.4.3.1
Combine and .
Step 3.4.3.2
Combine and .
Step 3.4.3.3
Multiply by .
Step 3.4.3.4
Combine and .
Step 3.4.3.5
Cancel the common factor of and .
Tap for more steps...
Step 3.4.3.5.1
Factor out of .
Step 3.4.3.5.2
Cancel the common factors.
Tap for more steps...
Step 3.4.3.5.2.1
Factor out of .
Step 3.4.3.5.2.2
Cancel the common factor.
Step 3.4.3.5.2.3
Rewrite the expression.
Step 3.4.3.5.2.4
Divide by .
Step 3.4.3.6
Combine and .
Step 3.4.3.7
Multiply by .
Step 3.4.3.8
Cancel the common factor of and .
Tap for more steps...
Step 3.4.3.8.1
Factor out of .
Step 3.4.3.8.2
Cancel the common factors.
Tap for more steps...
Step 3.4.3.8.2.1
Factor out of .
Step 3.4.3.8.2.2
Cancel the common factor.
Step 3.4.3.8.2.3
Rewrite the expression.
Step 3.4.3.8.2.4
Divide by .
Step 3.4.3.9
Move to the left of .
Step 3.4.3.10
Move .
Step 3.4.3.11
Add and .
Step 3.4.3.12
Subtract from .
Step 3.4.4
Reorder terms.
Step 3.4.5
Simplify each term.
Tap for more steps...
Step 3.4.5.1
Simplify the numerator.
Tap for more steps...
Step 3.4.5.1.1
Rewrite.
Step 3.4.5.1.2
Remove unnecessary parentheses.
Step 3.4.5.2
Move to the left of .
Step 3.4.6
Reorder factors in .
Step 4
Reform the equation by setting the left side equal to the right side.
Step 5
Replace with .