What is the derivative of (x-5)e^x ?

The derivative of (x-5)e^x is e^xx-4e^x

What is the first derivative of (x-5)e^x ?

The first derivative of (x-5)e^x is e^xx-4e^x

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derivative of

(x - 5) e^{x}

e^{x} x - 4 e^{x}

Solution steps

\frac{d}{d x} ((x - 5) e^{x})

Apply the Product Rule:

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

f = x - 5, g = e^{x}

= \frac{d}{d x} (x - 5) e^{x} + \frac{d}{d x} (e^{x}) (x - 5)

\frac{d}{d x} (x - 5) = 1

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

= 1 \cdot e^{x} + e^{x} (x - 5)

Simplify

1 \cdot e^{x} + e^{x} (x - 5) : e^{x} x - 4 e^{x}

= e^{x} x - 4 e^{x}

\frac{d}{d x} (\frac{cos ( x )}{x ^{5}})

\int sin^{5} (t) cos^{7} (t) d t

\frac{d}{d x} (arctanh (3 x))

ln (\frac{x ^{2}}{2 x ^{2} + 3 x + 2})

\int x - 25 - x^{2} d x

What is the derivative of (x-5)e^x ?
The derivative of (x-5)e^x is e^xx-4e^x
What is the first derivative of (x-5)e^x ?
The first derivative of (x-5)e^x is e^xx-4e^x