What is the derivative of f(x)=9x^8e^x+e^xx^9 ?

The derivative of f(x)=9x^8e^x+e^xx^9 is e^xx^9+18e^xx^8+72e^xx^7

What is the first derivative of f(x)=9x^8e^x+e^xx^9 ?

The first derivative of f(x)=9x^8e^x+e^xx^9 is e^xx^9+18e^xx^8+72e^xx^7

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derivative of

f (x) = 9 x^{8} e^{x} + e^{x} x^{9}

e^{x} x^{9} + 18 e^{x} x^{8} + 72 e^{x} x^{7}

Solution steps

\frac{d}{d x} (9 x^{8} e^{x} + e^{x} x^{9})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (9 x^{8} e^{x}) + \frac{d}{d x} (e^{x} x^{9})

\frac{d}{d x} (9 x^{8} e^{x}) = 9 (8 x^{7} e^{x} + e^{x} x^{8})

\frac{d}{d x} (e^{x} x^{9}) = e^{x} x^{9} + 9 x^{8} e^{x}

= 9 (8 x^{7} e^{x} + e^{x} x^{8}) + e^{x} x^{9} + 9 x^{8} e^{x}

Simplify

9 (8 x^{7} e^{x} + e^{x} x^{8}) + e^{x} x^{9} + 9 x^{8} e^{x} : e^{x} x^{9} + 18 e^{x} x^{8} + 72 e^{x} x^{7}

= e^{x} x^{9} + 18 e^{x} x^{8} + 72 e^{x} x^{7}

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What is the derivative of f(x)=9x^8e^x+e^xx^9 ?
The derivative of f(x)=9x^8e^x+e^xx^9 is e^xx^9+18e^xx^8+72e^xx^7
What is the first derivative of f(x)=9x^8e^x+e^xx^9 ?
The first derivative of f(x)=9x^8e^x+e^xx^9 is e^xx^9+18e^xx^8+72e^xx^7