What is the derivative of e^x(x-9) ?

The derivative of e^x(x-9) is e^xx-8e^x

What is the first derivative of e^x(x-9) ?

The first derivative of e^x(x-9) is e^xx-8e^x

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\frac{d}{d x} (e^{x} (x - 9))

e^{x} x - 8 e^{x}

Solution steps

\frac{d}{d x} (e^{x} (x - 9))

Apply the Product Rule:

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

f = e^{x}, g = x - 9

= \frac{d}{d x} (e^{x}) (x - 9) + \frac{d}{d x} (x - 9) e^{x}

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

\frac{d}{d x} (x - 9) = 1

= e^{x} (x - 9) + 1 \cdot e^{x}

Simplify

e^{x} (x - 9) + 1 \cdot e^{x} : e^{x} x - 8 e^{x}

= e^{x} x - 8 e^{x}

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

4 x^{2} + 10, 2 x + 7, - 3, 2

\frac{d}{d x} (3 x^{2} + \frac{1}{x ^{2}})

\int - \frac{1}{x - 4} d x

4 x - 32 x, at x = 4

What is the derivative of e^x(x-9) ?
The derivative of e^x(x-9) is e^xx-8e^x
What is the first derivative of e^x(x-9) ?
The first derivative of e^x(x-9) is e^xx-8e^x