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

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

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

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

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derivative of

y = 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) = \frac{cos ( x )}{x ^{6}}

\int (2 - sin (θ))^{2} d θ

\frac{2}{( s + 1 ) ^{2}}

\int 6 cos^{2} (x) d x

y^{^{''}} + 7 y^{^{'}} - 18 y = 0

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