What is the derivative of x^{11}e^x ?

The derivative of x^{11}e^x is 11x^{10}e^x+e^xx^{11}

What is the first derivative of x^{11}e^x ?

The first derivative of x^{11}e^x is 11x^{10}e^x+e^xx^{11}

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derivative of

x^{11} e^{x}

11 x^{10} e^{x} + e^{x} x^{11}

Solution steps

\frac{d}{d x} (x^{11} e^{x})

Apply the Product Rule:

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

f = x^{11}, g = e^{x}

= \frac{d}{d x} (x^{11}) e^{x} + \frac{d}{d x} (e^{x}) x^{11}

\frac{d}{d x} (x^{11}) = 11 x^{10}

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

= 11 x^{10} e^{x} + e^{x} x^{11}

x \to 0 lim (\frac{( 2 + x ) ^{2} - 4}{x})

\frac{d}{d x} (arccos (\frac{9}{x}))

\frac{\partial}{\partial y} (x y - z)

\frac{d ^{2}}{d x ^{2}} (e^{\frac{4}{x}})

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

What is the derivative of x^{11}e^x ?
The derivative of x^{11}e^x is 11x^{10}e^x+e^xx^{11}
What is the first derivative of x^{11}e^x ?
The first derivative of x^{11}e^x is 11x^{10}e^x+e^xx^{11}