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

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

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

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

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derivative of

y = 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}

\frac{\partial}{\partial x} (- 7 x^{2} + 7 y^{2} - 7)

\frac{\partial}{\partial y} (\frac{x + y}{1 + y ^{2}})

\frac{d}{d x} (- e^{- 5 x})

(2 + x^{2}) \frac{2 - x ^{2}}{2 - x}

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