What is the derivative of 9x^9e^{x-1} ?

The derivative of 9x^9e^{x-1} is 9(9x^8e^{x-1}+e^{x-1}x^9)

What is the first derivative of 9x^9e^{x-1} ?

The first derivative of 9x^9e^{x-1} is 9(9x^8e^{x-1}+e^{x-1}x^9)

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\frac{d}{d x} (9 x^{9} e^{x - 1})

9 (9 x^{8} e^{x - 1} + e^{x - 1} x^{9})

Solution steps

\frac{d}{d x} (9 x^{9} e^{x - 1})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 9 \frac{d}{d x} (x^{9} e^{x - 1})

Apply the Product Rule:

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

f = x^{9}, g = e^{x - 1}

= 9 (\frac{d}{d x} (x^{9}) e^{x - 1} + \frac{d}{d x} (e^{x - 1}) x^{9})

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

\frac{d}{d x} (e^{x - 1}) = e^{x - 1}

= 9 (9 x^{8} e^{x - 1} + e^{x - 1} x^{9})

What is the derivative of 9x^9e^{x-1} ?
The derivative of 9x^9e^{x-1} is 9(9x^8e^{x-1}+e^{x-1}x^9)
What is the first derivative of 9x^9e^{x-1} ?
The first derivative of 9x^9e^{x-1} is 9(9x^8e^{x-1}+e^{x-1}x^9)