What is the derivative of (X-1)e^X ?

The derivative of (X-1)e^X is e^XX

What is the first derivative of (X-1)e^X ?

The first derivative of (X-1)e^X is e^XX

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derivative of

(X - 1) e^{X}

e^{X} X

Solution steps

\frac{d}{d X} ((X - 1) e^{X})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = X - 1, g = e^{X}

= \frac{d}{d X} (X - 1) e^{X} + \frac{d}{d X} (e^{X}) (X - 1)

\frac{d}{d X} (X - 1) = 1

\frac{d}{d X} (e^{X}) = e^{X}

= 1 \cdot e^{X} + e^{X} (X - 1)

Simplify

1 \cdot e^{X} + e^{X} (X - 1) : e^{X} X

= e^{X} X

\frac{d y}{d x}, 4 y^{2} + 2 = 3 x^{2}

\int \frac{- 1}{x ^{2}} d x

\int \frac{1}{x ^{2} + 2 x + 101} d x

x \to 0 lim (\frac{x ^{2} + 4 x - 2}{x})

e^{- 2 t} sin (2 t)

What is the derivative of (X-1)e^X ?
The derivative of (X-1)e^X is e^XX
What is the first derivative of (X-1)e^X ?
The first derivative of (X-1)e^X is e^XX