What is the derivative of f(x)=(x-1)e^x ?

The derivative of f(x)=(x-1)e^x is e^xx

What is the first derivative of f(x)=(x-1)e^x ?

The first derivative of f(x)=(x-1)e^x is e^xx

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derivative of

f (x) = (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

x \to 1 - lim (2^{\frac{1}{x - 2}})

\int \frac{9 - x ^{2}}{x ^{2}} d x

y^{^{'}} = t^{0.5}, y (0) = 0

\frac{d}{d x} (5 x e^{3 x})

\int_{0}^{\frac{π}{3}} 8 sec^{3} (x) d x

What is the derivative of f(x)=(x-1)e^x ?
The derivative of f(x)=(x-1)e^x is e^xx
What is the first derivative of f(x)=(x-1)e^x ?
The first derivative of f(x)=(x-1)e^x is e^xx