What is the derivative of f(x)=(2-x)e^x ?

The derivative of f(x)=(2-x)e^x is e^x-e^xx

What is the first derivative of f(x)=(2-x)e^x ?

The first derivative of f(x)=(2-x)e^x is e^x-e^xx

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derivative of

f (x) = (2 - x) e^{x}

e^{x} - e^{x} x

Solution steps

\frac{d}{d x} ((2 - x) e^{x})

Apply the Product Rule:

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

f = 2 - x, g = e^{x}

= \frac{d}{d x} (2 - x) e^{x} + \frac{d}{d x} (e^{x}) (2 - x)

\frac{d}{d x} (2 - x) = - 1

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

= (- 1) e^{x} + e^{x} (2 - x)

Simplify

(- 1) e^{x} + e^{x} (2 - x) : e^{x} - e^{x} x

= e^{x} - e^{x} x

x \to 0 + lim (2)

t

x \to \infty lim (- (x^{2}))

\frac{d}{d x} (\frac{2 ( 1 - x ^{2} )}{( 1 + x ^{2} ) ^{2}})

\int_{- 5}^{5} π (25 - x^{2}) d x

What is the derivative of f(x)=(2-x)e^x ?
The derivative of f(x)=(2-x)e^x is e^x-e^xx
What is the first derivative of f(x)=(2-x)e^x ?
The first derivative of f(x)=(2-x)e^x is e^x-e^xx