What is the derivative of f(x)=x^9e^x ?

The derivative of f(x)=x^9e^x is 9x^8e^x+e^xx^9

What is the first derivative of f(x)=x^9e^x ?

The first derivative of f(x)=x^9e^x is 9x^8e^x+e^xx^9

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derivative of

f (x) = 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}

y^{\frac{1}{2}} y^{^{'}} + y^{\frac{3}{2}} = 1

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

x^{2} + 2 x + 1, 2 x + 5

f (n) = 3^{n}

\int \frac{x ^{3}}{5 x ^{2} + 9} d x

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