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Popular >

derivative of (6x^2-9xe^x)

Solution

\frac{d}{d x} ((6 x^{2} - 9 x) e^{x})

Solution

6 e^{x} x^{2} + 3 e^{x} x - 9 e^{x}

Solution steps

\frac{d}{d x} ((6 x^{2} - 9 x) e^{x})

Apply the Product Rule:

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

f = 6 x^{2} - 9 x, g = e^{x}

= \frac{d}{d x} (6 x^{2} - 9 x) e^{x} + \frac{d}{d x} (e^{x}) (6 x^{2} - 9 x)

\frac{d}{d x} (6 x^{2} - 9 x) = 12 x - 9

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

= (12 x - 9) e^{x} + e^{x} (6 x^{2} - 9 x)

Simplify

(12 x - 9) e^{x} + e^{x} (6 x^{2} - 9 x) : 6 e^{x} x^{2} + 3 e^{x} x - 9 e^{x}

= 6 e^{x} x^{2} + 3 e^{x} x - 9 e^{x}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (6x^2-9xe^x) ?
The derivative of (6x^2-9xe^x) is 6e^xx^2+3e^xx-9e^x
What is the first derivative of (6x^2-9xe^x) ?
The first derivative of (6x^2-9xe^x) is 6e^xx^2+3e^xx-9e^x