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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

2 e^{z}

\frac{d}{d x} (\frac{3 x - 7}{2 x + 4})

f (x) = \frac{7 + tan ( x )}{5 - tan ( x )}

\frac{\partial}{\partial x} (- 3 y cos (3 x))

(x y^{2} - 3 y) d x + (x^{2} y - 3 x) d y = 0

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