What is the derivative of y=x^9e^x ?

The derivative of y=x^9e^x is 9x^8e^x+e^xx^9

What is the first derivative of y=x^9e^x ?

The first derivative of y=x^9e^x is 9x^8e^x+e^xx^9

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derivative of

y = x^{9} e^{x}

9 x^{8} e^{x} + e^{x} x^{9}

Solution steps

\frac{d}{d x} (x^{9} e^{x})

Apply the Product Rule:

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

f = x^{9}, g = e^{x}

= \frac{d}{d x} (x^{9}) e^{x} + \frac{d}{d x} (e^{x}) x^{9}

\frac{d}{d x} (x^{9}) = 9 x^{8}

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

= 9 x^{8} e^{x} + e^{x} x^{9}

\int 12 (e^{0.02 x} - 1) d x

\int \frac{1}{9 e ^{- 2 u} - 1} d u

2 x^{- 5}

\int - 2 cos (x) d x

\int_{1}^{6} x - 1 d x

What is the derivative of y=x^9e^x ?
The derivative of y=x^9e^x is 9x^8e^x+e^xx^9
What is the first derivative of y=x^9e^x ?
The first derivative of y=x^9e^x is 9x^8e^x+e^xx^9