What is the derivative of y=x^7e^x ?

The derivative of y=x^7e^x is 7x^6e^x+e^xx^7

What is the first derivative of y=x^7e^x ?

The first derivative of y=x^7e^x is 7x^6e^x+e^xx^7

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derivative of

y = x^{7} e^{x}

7 x^{6} e^{x} + e^{x} x^{7}

Solution steps

\frac{d}{d x} (x^{7} e^{x})

Apply the Product Rule:

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

f = x^{7}, g = e^{x}

= \frac{d}{d x} (x^{7}) e^{x} + \frac{d}{d x} (e^{x}) x^{7}

\frac{d}{d x} (x^{7}) = 7 x^{6}

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

= 7 x^{6} e^{x} + e^{x} x^{7}

What is the derivative of y=x^7e^x ?
The derivative of y=x^7e^x is 7x^6e^x+e^xx^7
What is the first derivative of y=x^7e^x ?
The first derivative of y=x^7e^x is 7x^6e^x+e^xx^7