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

The derivative of 9x^8e^x+x^9e^x is 72e^xx^7+18e^xx^8+e^xx^9

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

The first derivative of 9x^8e^x+x^9e^x is 72e^xx^7+18e^xx^8+e^xx^9

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derivative of

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

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

\int 16 e^{- 4 x} sin (4 x) d x

- 6 s

x \to - 3 lim (\frac{1}{x ^{2} - 9})

\frac{1}{2 + x}, 0

y^{^{''}} + y = 5 sin (x)

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