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Popular >

derivative of y=(x^2-8x)e^x

Solution

derivative of

y = (x^{2} - 8 x) e^{x}

Solution

e^{x} x^{2} - 6 e^{x} x - 8 e^{x}

Solution steps

\frac{d}{d x} ((x^{2} - 8 x) e^{x})

Apply the Product Rule:

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

f = x^{2} - 8 x, g = e^{x}

= \frac{d}{d x} (x^{2} - 8 x) e^{x} + \frac{d}{d x} (e^{x}) (x^{2} - 8 x)

\frac{d}{d x} (x^{2} - 8 x) = 2 x - 8

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

= (2 x - 8) e^{x} + e^{x} (x^{2} - 8 x)

Simplify

(2 x - 8) e^{x} + e^{x} (x^{2} - 8 x) : e^{x} x^{2} - 6 e^{x} x - 8 e^{x}

= e^{x} x^{2} - 6 e^{x} x - 8 e^{x}

Popular Examples

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derivative of f(x)=(20x)/(x^2-5)derivative of

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inverse oflaplace 2/(s+2)inverse laplace

\frac{2}{s + 2}

Frequently Asked Questions (FAQ)

What is the derivative of y=(x^2-8x)e^x ?
The derivative of y=(x^2-8x)e^x is e^xx^2-6e^xx-8e^x
What is the first derivative of y=(x^2-8x)e^x ?
The first derivative of y=(x^2-8x)e^x is e^xx^2-6e^xx-8e^x