Derivative of x*e^(2x)
Answer
e^(2*x)+2*e^(2*x)*x
Derivative of x*e^(2x)
- 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^(2*x) is e^(2*x)+2*e^(2*x)*x.
Instant step-by-step solution for x*e^(2x)
Share this result
Derivative of x*e^(2x) = e^(2*x)+2*e^(2*x)*x Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-xe-minus-to-minus-the-minus-2x
How to find the derivative of x*e^(2x)
To find the derivative of x*e^(2x), we use standard differentiation rules. Our AI-powered calculator breaks down the steps and explains the logic.
Practice More Problems
Derivative of cosh(x)
Solve d/dx cosh(x)
Derivative of cot(x)
Solve d/dx cot(x)
Derivative of csc(x)
Solve d/dx csc(x)
Derivative of ln(2x)
Solve d/dx ln(2x)
Derivative of ln(x)
Solve d/dx ln(x)
Derivative of -x
Solve d/dx -x
Derivative of x^(1/2)
Solve d/dx x^(1/2)
Derivative of sec(x)
Solve d/dx sec(x)
Derivative of sin(2x)
Solve d/dx sin(2x)
Frequently Asked Questions
What is the derivative of x*e^(2x)?▼
The derivative of x*e^(2x) is e^(2*x)+2*e^(2*x)*x.
How do you find the derivative of x*e^(2x)?▼
Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is e^(2*x)+2*e^(2*x)*x.
Why is the derivative of x*e^(2x) equal to e^(2*x)+2*e^(2*x)*x?▼
Because differentiation measures how a function changes — applying the rules to x*e^(2x) yields e^(2*x)+2*e^(2*x)*x. See the full step-by-step breakdown above.