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Popular >

derivative of (4x^2-6xe^x)

Solution

\frac{d}{d x} ((4 x^{2} - 6 x) e^{x})

Solution

4 e^{x} x^{2} + 2 e^{x} x - 6 e^{x}

Solution steps

\frac{d}{d x} ((4 x^{2} - 6 x) e^{x})

Apply the Product Rule:

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

f = 4 x^{2} - 6 x, g = e^{x}

= \frac{d}{d x} (4 x^{2} - 6 x) e^{x} + \frac{d}{d x} (e^{x}) (4 x^{2} - 6 x)

\frac{d}{d x} (4 x^{2} - 6 x) = 8 x - 6

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

= (8 x - 6) e^{x} + e^{x} (4 x^{2} - 6 x)

Simplify

(8 x - 6) e^{x} + e^{x} (4 x^{2} - 6 x) : 4 e^{x} x^{2} + 2 e^{x} x - 6 e^{x}

= 4 e^{x} x^{2} + 2 e^{x} x - 6 e^{x}

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Frequently Asked Questions (FAQ)

What is the derivative of (4x^2-6xe^x) ?
The derivative of (4x^2-6xe^x) is 4e^xx^2+2e^xx-6e^x
What is the first derivative of (4x^2-6xe^x) ?
The first derivative of (4x^2-6xe^x) is 4e^xx^2+2e^xx-6e^x