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Popular >

derivative of 3x*e^{2x}

Solution

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

Solution

3 (e^{2 x} + 2 e^{2 x} x)

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} (e^{2 x}) = e^{2 x} \cdot 2

= 3 (1 \cdot e^{2 x} + e^{2 x} \cdot 2 x)

Simplify

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

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x \to \infty lim (\frac{e ^{\frac{1}{x}}}{arctan ( x )})

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\int 7 x sin (x) d x

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\frac{10}{s ^{2}}

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\frac{\partial}{\partial x} (1 0^{x^{2} - 1})

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\int \frac{1}{2 x ln ( x )} d x

Frequently Asked Questions (FAQ)

What is the derivative of 3x*e^{2x} ?
The derivative of 3x*e^{2x} is 3(e^{2x}+2e^{2x}x)
What is the first derivative of 3x*e^{2x} ?
The first derivative of 3x*e^{2x} is 3(e^{2x}+2e^{2x}x)