Derivative of x*e^(9x)
Answer
e^(9*x)+9*e^(9*x)*x
Derivative of x*e^(9x)
- Rule Used
- Product Rule
- Steps
- Identify a product of two functions of x in x*: use the product rule (uv)' = u'v + uv'. Each factor is differentiated once while the other is held as-is, then the two terms are added.
- Differentiate each factor and combine.
- Final answer: +*x
The derivative of x*e^(9*x) is e^(9*x)+9*e^(9*x)*x.
Instant step-by-step solution for x*e^(9x)
Share this result
Derivative of x*e^(9x) = e^(9*x)+9*e^(9*x)*x Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-xe-minus-to-minus-the-minus-9x
How to find the derivative of x*e^(9x)
To find the derivative of x*e^(9x), we use standard differentiation rules. Our AI-powered calculator breaks down the steps and explains the logic.
Practice More Problems
Derivative of x*sin(x)
Solve d/dx x*sin(x)
Derivative of x^2
Solve d/dx x^2
Derivative of x^2-1
Solve d/dx x^2-1
Derivative of x^2+1
Solve d/dx x^2+1
Derivative of x^4
Solve d/dx x^4
Derivative of 10^x
Solve d/dx 10^x
Derivative of 2^x
Solve d/dx 2^x
Derivative of e^(2x)
Solve d/dx e^(2x)
Derivative of e^(-x)
Solve d/dx e^(-x)
Derivative of e^x
Solve d/dx e^x
Frequently Asked Questions
What is the derivative of x*e^(9x)?▼
The derivative of x*e^(9x) is e^(9*x)+9*e^(9*x)*x.
How do you find the derivative of x*e^(9x)?▼
Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is e^(9*x)+9*e^(9*x)*x.
Why is the derivative of x*e^(9x) equal to e^(9*x)+9*e^(9*x)*x?▼
Because differentiation measures how a function changes — applying the rules to x*e^(9x) yields e^(9*x)+9*e^(9*x)*x. See the full step-by-step breakdown above.