What is the derivative of (3x^2-5x)e^x ?

The derivative of (3x^2-5x)e^x is 3e^xx^2+e^xx-5e^x

What is the first derivative of (3x^2-5x)e^x ?

The first derivative of (3x^2-5x)e^x is 3e^xx^2+e^xx-5e^x

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derivative of

(3 x^{2} - 5 x) e^{x}

3 e^{x} x^{2} + e^{x} x - 5 e^{x}

Solution steps

\frac{d}{d x} ((3 x^{2} - 5 x) e^{x})

Apply the Product Rule:

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

f = 3 x^{2} - 5 x, g = e^{x}

= \frac{d}{d x} (3 x^{2} - 5 x) e^{x} + \frac{d}{d x} (e^{x}) (3 x^{2} - 5 x)

\frac{d}{d x} (3 x^{2} - 5 x) = 6 x - 5

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

= (6 x - 5) e^{x} + e^{x} (3 x^{2} - 5 x)

Simplify

(6 x - 5) e^{x} + e^{x} (3 x^{2} - 5 x) : 3 e^{x} x^{2} + e^{x} x - 5 e^{x}

= 3 e^{x} x^{2} + e^{x} x - 5 e^{x}

x \to 0 + lim (- \frac{1}{x})

\frac{d y}{d t} = - y^{2}, y (0) = \frac{1}{2}

\int e^{5 x} \cdot 3 e^{5 x} + 2 d x

x \to 0 + lim ((1 + a x)^{\frac{1}{x}})

\frac{\partial}{\partial x} (e^{y} (x^{2} - y^{2}))

What is the derivative of (3x^2-5x)e^x ?
The derivative of (3x^2-5x)e^x is 3e^xx^2+e^xx-5e^x
What is the first derivative of (3x^2-5x)e^x ?
The first derivative of (3x^2-5x)e^x is 3e^xx^2+e^xx-5e^x