What is the derivative of (9x^2-18x+18e^x) ?

The derivative of (9x^2-18x+18e^x) is 9e^xx^2

What is the first derivative of (9x^2-18x+18e^x) ?

The first derivative of (9x^2-18x+18e^x) is 9e^xx^2

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\frac{d}{d x} ((9 x^{2} - 18 x + 18) e^{x})

9 e^{x} x^{2}

Solution steps

\frac{d}{d x} ((9 x^{2} - 18 x + 18) e^{x})

Apply the Product Rule:

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

f = 9 x^{2} - 18 x + 18, g = e^{x}

= \frac{d}{d x} (9 x^{2} - 18 x + 18) e^{x} + \frac{d}{d x} (e^{x}) (9 x^{2} - 18 x + 18)

\frac{d}{d x} (9 x^{2} - 18 x + 18) = 18 x - 18

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

= (18 x - 18) e^{x} + e^{x} (9 x^{2} - 18 x + 18)

Simplify

(18 x - 18) e^{x} + e^{x} (9 x^{2} - 18 x + 18) : 9 e^{x} x^{2}

= 9 e^{x} x^{2}

What is the derivative of (9x^2-18x+18e^x) ?
The derivative of (9x^2-18x+18e^x) is 9e^xx^2
What is the first derivative of (9x^2-18x+18e^x) ?
The first derivative of (9x^2-18x+18e^x) is 9e^xx^2