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Popular >

derivative of-e^x(x+5)

Solution

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

Solution

- e^{x} x - 6 e^{x}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - \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 - 6 e^{x}

= - e^{x} x - 6 e^{x}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of-e^x(x+5) ?
The derivative of-e^x(x+5) is -e^xx-6e^x
What is the first derivative of-e^x(x+5) ?
The first derivative of-e^x(x+5) is -e^xx-6e^x