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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

(t \cdot e^{t})^{^{'}}

\frac{d y}{d x} = \frac{2 y}{x ^{2}}

f (x) = a^{x}

x \to 2 lim (3 x^{2} + 5 x)

\frac{\partial}{\partial x} (e^{a x})

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