Calculus • Step-by-Step

Derivative of x · eˣ with Steps

Differentiate x·eˣ step by step using the Product Rule. Detailed working with u = x and v = e^x, showing full substitution to yield e^x(x + 1).

Problem Statement

\frac{d}{dx}[x e^x]

Final Result

f'(x) = e^{x} \cdot x+e^{x}

Formula Required: Product Rule

Let u = x and v = e^x. Then u' = 1 and v' = e^x.

\frac{d}{dx}[u \cdot v] = u'v + uv'

2 Steps

Set up the differentiation problem with respect to variable $x$.

\frac{d}{dx} \left[ e^{x} \cdot x \right]

Apply the Product Rule to compute the derivative.

\frac{d}{dx} \left[ e^{x} \cdot x \right] = e^{x} \cdot x+e^{x}

Interactive Calculator

Enter any equation like 2x + 8 = 20 or x² - 5x + 6 = 0 to get step-by-step solutions.

Using the product rule: (1)(e^x) + (x)(e^x) = e^x(1 + x).