What is the derivative of 9x^8e^x+e^{xx^9} ?

The derivative of 9x^8e^x+e^{xx^9} is 9(e^xx^8+8x^7e^x)+e^{x^{10}}*10x^9

What is the first derivative of 9x^8e^x+e^{xx^9} ?

The first derivative of 9x^8e^x+e^{xx^9} is 9(e^xx^8+8x^7e^x)+e^{x^{10}}*10x^9

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

9 (e^{x} x^{8} + 8 x^{7} e^{x}) + e^{x^{10}} \cdot 10 x^{9}

Solution steps

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

Simplify

9 x^{8} e^{x} + e^{x x^{9}} : 9 e^{x} x^{8} + e^{x^{10}}

= \frac{d}{d x} (9 e^{x} x^{8} + e^{x^{10}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (9 e^{x} x^{8}) + \frac{d}{d x} (e^{x^{10}})

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

\frac{d}{d x} (e^{x^{10}}) = e^{x^{10}} \cdot 10 x^{9}

= 9 (e^{x} x^{8} + 8 x^{7} e^{x}) + e^{x^{10}} \cdot 10 x^{9}

What is the derivative of 9x^8e^x+e^{xx^9} ?
The derivative of 9x^8e^x+e^{xx^9} is 9(e^xx^8+8x^7e^x)+e^{x^{10}}*10x^9
What is the first derivative of 9x^8e^x+e^{xx^9} ?
The first derivative of 9x^8e^x+e^{xx^9} is 9(e^xx^8+8x^7e^x)+e^{x^{10}}*10x^9