What is the derivative of 8x^7e^x+e^xx^8 ?

The derivative of 8x^7e^x+e^xx^8 is e^xx^8+16e^xx^7+56e^xx^6

What is the first derivative of 8x^7e^x+e^xx^8 ?

The first derivative of 8x^7e^x+e^xx^8 is e^xx^8+16e^xx^7+56e^xx^6

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derivative of

8 x^{7} e^{x} + e^{x} x^{8}

e^{x} x^{8} + 16 e^{x} x^{7} + 56 e^{x} x^{6}

Solution steps

\frac{d}{d x} (8 x^{7} e^{x} + e^{x} x^{8})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (8 x^{7} e^{x}) + \frac{d}{d x} (e^{x} x^{8})

\frac{d}{d x} (8 x^{7} e^{x}) = 8 (7 x^{6} e^{x} + e^{x} x^{7})

\frac{d}{d x} (e^{x} x^{8}) = e^{x} x^{8} + 8 x^{7} e^{x}

= 8 (7 x^{6} e^{x} + e^{x} x^{7}) + e^{x} x^{8} + 8 x^{7} e^{x}

Simplify

8 (7 x^{6} e^{x} + e^{x} x^{7}) + e^{x} x^{8} + 8 x^{7} e^{x} : e^{x} x^{8} + 16 e^{x} x^{7} + 56 e^{x} x^{6}

= e^{x} x^{8} + 16 e^{x} x^{7} + 56 e^{x} x^{6}

What is the derivative of 8x^7e^x+e^xx^8 ?
The derivative of 8x^7e^x+e^xx^8 is e^xx^8+16e^xx^7+56e^xx^6
What is the first derivative of 8x^7e^x+e^xx^8 ?
The first derivative of 8x^7e^x+e^xx^8 is e^xx^8+16e^xx^7+56e^xx^6