What is the derivative of (3x^2-4x)e^x ?

The derivative of (3x^2-4x)e^x is 3e^xx^2+2e^xx-4e^x

What is the first derivative of (3x^2-4x)e^x ?

The first derivative of (3x^2-4x)e^x is 3e^xx^2+2e^xx-4e^x

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derivative of

(3 x^{2} - 4 x) e^{x}

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

Solution steps

\frac{d}{d x} ((3 x^{2} - 4 x) e^{x})

Apply the Product Rule:

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

f = 3 x^{2} - 4 x, g = e^{x}

= \frac{d}{d x} (3 x^{2} - 4 x) e^{x} + \frac{d}{d x} (e^{x}) (3 x^{2} - 4 x)

\frac{d}{d x} (3 x^{2} - 4 x) = 6 x - 4

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

= (6 x - 4) e^{x} + e^{x} (3 x^{2} - 4 x)

Simplify

(6 x - 4) e^{x} + e^{x} (3 x^{2} - 4 x) : 3 e^{x} x^{2} + 2 e^{x} x - 4 e^{x}

= 3 e^{x} x^{2} + 2 e^{x} x - 4 e^{x}

What is the derivative of (3x^2-4x)e^x ?
The derivative of (3x^2-4x)e^x is 3e^xx^2+2e^xx-4e^x
What is the first derivative of (3x^2-4x)e^x ?
The first derivative of (3x^2-4x)e^x is 3e^xx^2+2e^xx-4e^x