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

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

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

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

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derivative of

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}

x \to 2 + lim (\frac{3 + x}{2 - x})

\frac{d}{d x} (ln (1 0^{- x} - 1))

\int e^{x^{2}} \cdot x^{3} d x

\frac{d}{d x} ((x^{2} - 3 x + 1)^{4})

5 x, \frac{5}{3} x, 14 - x^{2}

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