What is the derivative of f(x)=2xe^{7x} ?

The derivative of f(x)=2xe^{7x} is 2(e^{7x}+7e^{7x}x)

What is the first derivative of f(x)=2xe^{7x} ?

The first derivative of f(x)=2xe^{7x} is 2(e^{7x}+7e^{7x}x)

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derivative of

f (x) = 2 x e^{7 x}

2 (e^{7 x} + 7 e^{7 x} x)

Solution steps

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

Take the constant out:

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

= 2 \frac{d}{d x} (x e^{7 x})

Apply the Product Rule:

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

f = x, g = e^{7 x}

= 2 (\frac{d x}{d x} e^{7 x} + \frac{d}{d x} (e^{7 x}) x)

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

\frac{d}{d x} (e^{7 x}) = e^{7 x} \cdot 7

= 2 (1 \cdot e^{7 x} + e^{7 x} \cdot 7 x)

Simplify

= 2 (e^{7 x} + 7 e^{7 x} x)

f (y) = 1 - y^{2}

sin (\frac{1}{x ^{2}})

f^{^{''}} (x) = 9 x^{3} + 4 x^{2} + 7 x

x \to 0 lim (∣ x - 2 ∣ + 3)

\frac{\partial}{\partial y} (sin (y) cos (y))

What is the derivative of f(x)=2xe^{7x} ?
The derivative of f(x)=2xe^{7x} is 2(e^{7x}+7e^{7x}x)
What is the first derivative of f(x)=2xe^{7x} ?
The first derivative of f(x)=2xe^{7x} is 2(e^{7x}+7e^{7x}x)