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

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

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

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

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derivative of

f (x) = e^{x} (1 - x)

- e^{x} x

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

= - e^{x} x

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