What is the derivative of x^6e^x ?

The derivative of x^6e^x is 6x^5e^x+e^xx^6

What is the first derivative of x^6e^x ?

The first derivative of x^6e^x is 6x^5e^x+e^xx^6

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derivative of

x^{6} e^{x}

6 x^{5} e^{x} + e^{x} x^{6}

Solution steps

\frac{d}{d x} (x^{6} e^{x})

Apply the Product Rule:

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

f = x^{6}, g = e^{x}

= \frac{d}{d x} (x^{6}) e^{x} + \frac{d}{d x} (e^{x}) x^{6}

\frac{d}{d x} (x^{6}) = 6 x^{5}

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

= 6 x^{5} e^{x} + e^{x} x^{6}

f (x) = 4 x^{2} + 2 x, (- 3, 30)

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

(x - 3) 4 - x

\frac{d}{d x} ((1 - x^{3})^{\frac{1}{2}})

ln (x), 5

What is the derivative of x^6e^x ?
The derivative of x^6e^x is 6x^5e^x+e^xx^6
What is the first derivative of x^6e^x ?
The first derivative of x^6e^x is 6x^5e^x+e^xx^6