What is the derivative of e^x(x-3) ?

The derivative of e^x(x-3) is e^xx-2e^x

What is the first derivative of e^x(x-3) ?

The first derivative of e^x(x-3) is e^xx-2e^x

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

e^{x} x - 2 e^{x}

Solution steps

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

Apply the Product Rule:

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

f = e^{x}, g = x - 3

= \frac{d}{d x} (e^{x}) (x - 3) + \frac{d}{d x} (x - 3) e^{x}

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

\frac{d}{d x} (x - 3) = 1

= e^{x} (x - 3) + 1 \cdot e^{x}

Simplify

e^{x} (x - 3) + 1 \cdot e^{x} : e^{x} x - 2 e^{x}

= e^{x} x - 2 e^{x}

\int 8 (tan^{2} (x) + tan^{4} (x)) d x

x, \frac{1}{2} x, 9

x \to - 1 + lim (2 x^{3} - 2 m)

f (x) = 5 e^{2 x}

\frac{d y}{d x} = \frac{e ^{x}}{8 + e ^{x}}

What is the derivative of e^x(x-3) ?
The derivative of e^x(x-3) is e^xx-2e^x
What is the first derivative of e^x(x-3) ?
The first derivative of e^x(x-3) is e^xx-2e^x