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

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

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

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

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

- e^{x} x

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

= - e^{x} x

(cos (x))^{2}

x \to 2 lim (3 e^{x - 2})

\int sin^{9} (x) cos^{6} (x) d x

(48) (4 - 4)

\int e^{(1 - s) t} d t

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