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Popular >

derivative of (3x^2-4x)e^x

Solution

derivative of

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

Solution

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}

Popular Examples

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\int \frac{1}{t 2 t ^{2} - 9} d t

limit as x approaches 0 of ((tan(3x)))/x

x \to 0 lim (\frac{( tan ( 3 x ) )}{x})

(\partial)/(\partial y)(sin(x^2-y))

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

integral of (tan^3(x))

\int (tan^{3} (x)) d x

area y=x^2,y=x+2,0 area

y = x^{2}, y = x + 2, 0

Frequently Asked Questions (FAQ)

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