What is the derivative of y=x^8e^x ?

The derivative of y=x^8e^x is 8x^7e^x+e^xx^8

What is the first derivative of y=x^8e^x ?

The first derivative of y=x^8e^x is 8x^7e^x+e^xx^8

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derivative of

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

8 x^{7} e^{x} + e^{x} x^{8}

Solution steps

\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}

= \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}

= 8 x^{7} e^{x} + e^{x} x^{8}

\frac{d}{d x} ((\frac{d x}{d x})^{2})

y = 8 x^{2} - x^{3}, (2, 24)

\int ln (2 t) d t

y = (\frac{2 x ^{2}}{6 - x})^{3}

\int \frac{x ^{3} + 2 x ^{2} + 5 x + 1}{x ^{2} + 2 x + 5} d x

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