What is the derivative of f(x)=2xe^{4x} ?

The derivative of f(x)=2xe^{4x} is 2(e^{4x}+4e^{4x}x)

What is the first derivative of f(x)=2xe^{4x} ?

The first derivative of f(x)=2xe^{4x} is 2(e^{4x}+4e^{4x}x)

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derivative of

f (x) = 2 x e^{4 x}

2 (e^{4 x} + 4 e^{4 x} x)

Solution steps

\frac{d}{d x} (2 x e^{4 x})

Take the constant out:

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

= 2 \frac{d}{d x} (x e^{4 x})

Apply the Product Rule:

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

f = x, g = e^{4 x}

= 2 (\frac{d x}{d x} e^{4 x} + \frac{d}{d x} (e^{4 x}) x)

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

\frac{d}{d x} (e^{4 x}) = e^{4 x} \cdot 4

= 2 (1 \cdot e^{4 x} + e^{4 x} \cdot 4 x)

Simplify

= 2 (e^{4 x} + 4 e^{4 x} x)

n = 0 \sum \infty \frac{n ( n + 1 )}{2}

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

\int_{0}^{\frac{1}{2}} cos (π x) d x

(2 x y + 3 y^{2}) d x - (x^{2} + 2 x y) d y = 0

f (x) = 34 x - 16 x^{2}, at x = 1

What is the derivative of f(x)=2xe^{4x} ?
The derivative of f(x)=2xe^{4x} is 2(e^{4x}+4e^{4x}x)
What is the first derivative of f(x)=2xe^{4x} ?
The first derivative of f(x)=2xe^{4x} is 2(e^{4x}+4e^{4x}x)