Derivative of x*e^(14*x)
Answer
e^(14*x)+14*e^(14*x)*x
Derivative of x*e^(14*x)
- 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^(14*x) is e^(14*x)+14*e^(14*x)*x.
Instant step-by-step solution for x*e^(14*x)
Share this result
Derivative of x*e^(14*x) = e^(14*x)+14*e^(14*x)*x Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-xe-minus-to-minus-the-minus-14x
How to find the derivative of x*e^(14*x)
To find the derivative of x*e^(14*x), we use standard differentiation rules. Our AI-powered calculator breaks down the steps and explains the logic.
Practice More Problems
Derivative of acos(x)
Solve d/dx acos(x)
Derivative of asin(x)
Solve d/dx asin(x)
Derivative of atan(x)
Solve d/dx atan(x)
Derivative of x^(1/3)
Solve d/dx x^(1/3)
Derivative of cos(2x)
Solve d/dx cos(2x)
Derivative of cos(x)^2
Solve d/dx cos(x)^2
Derivative of cos(x)
Solve d/dx cos(x)
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)
Frequently Asked Questions
What is the derivative of x*e^(14*x)?▼
The derivative of x*e^(14*x) is e^(14*x)+14*e^(14*x)*x.
How do you find the derivative of x*e^(14*x)?▼
Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is e^(14*x)+14*e^(14*x)*x.
Why is the derivative of x*e^(14*x) equal to e^(14*x)+14*e^(14*x)*x?▼
Because differentiation measures how a function changes — applying the rules to x*e^(14*x) yields e^(14*x)+14*e^(14*x)*x. See the full step-by-step breakdown above.