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Popular >

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

Solution

\frac{d}{d x} ((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

integral of (4x^3-7x-12)/(x^3-x^2-6x)

\int \frac{4 x ^{3} - 7 x - 12}{x ^{3} - x ^{2} - 6 x} d x

integral of 15sin^2(x)cos^3(x)

\int 15 sin^{2} (x) cos^{3} (x) d x

derivative of 7/(2x)

\frac{d}{d x} (\frac{7}{2 x})

limit as x approaches-1 of 4x^3+x^2+2x+1

x \to - 1 lim (4 x^{3} + x^{2} + 2 x + 1)

(dy)/(dx)=yx^9sin(x^{10})

\frac{d y}{d x} = y x^{9} sin (x^{10})

Frequently Asked Questions (FAQ)

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