What is the derivative of x^{12}e^x ?

The derivative of x^{12}e^x is 12x^{11}e^x+e^xx^{12}

What is the first derivative of x^{12}e^x ?

The first derivative of x^{12}e^x is 12x^{11}e^x+e^xx^{12}

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derivative of

x^{12} e^{x}

12 x^{11} e^{x} + e^{x} x^{12}

Solution steps

\frac{d}{d x} (x^{12} e^{x})

Apply the Product Rule:

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

f = x^{12}, g = e^{x}

= \frac{d}{d x} (x^{12}) e^{x} + \frac{d}{d x} (e^{x}) x^{12}

\frac{d}{d x} (x^{12}) = 12 x^{11}

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

= 12 x^{11} e^{x} + e^{x} x^{12}

f (x) = - x^{2} + 2 x

f (x) = \frac{1}{10} x (x - 2) (x - 3)

f (x) = 5 x

\frac{d}{d x} (27 cos (3 x))

\int_{1}^{6} t^{4} ln (2 t) d t

What is the derivative of x^{12}e^x ?
The derivative of x^{12}e^x is 12x^{11}e^x+e^xx^{12}
What is the first derivative of x^{12}e^x ?
The first derivative of x^{12}e^x is 12x^{11}e^x+e^xx^{12}