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Popular >

derivative of y=5x^8e^x

Solution

derivative of

y = 5 x^{8} e^{x}

Solution

5 (8 x^{7} e^{x} + e^{x} x^{8})

Solution steps

\frac{d}{d x} (5 x^{8} e^{x})

Take the constant out:

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

= 5 \frac{d}{d x} (x^{8} e^{x})

Apply the Product Rule:

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

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

= 5 (\frac{d}{d x} (x^{8}) e^{x} + \frac{d}{d x} (e^{x}) x^{8})

\frac{d}{d x} (x^{8}) = 8 x^{7}

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

= 5 (8 x^{7} e^{x} + e^{x} x^{8})

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Frequently Asked Questions (FAQ)

What is the derivative of y=5x^8e^x ?
The derivative of y=5x^8e^x is 5(8x^7e^x+e^xx^8)
What is the first derivative of y=5x^8e^x ?
The first derivative of y=5x^8e^x is 5(8x^7e^x+e^xx^8)