What is the derivative of xe^{7x} ?

The derivative of xe^{7x} is e^{7x}+7e^{7x}x

What is the first derivative of xe^{7x} ?

The first derivative of xe^{7x} is e^{7x}+7e^{7x}x

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

e^{7 x} + 7 e^{7 x} x

Solution steps

\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}

= \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

= 1 \cdot e^{7 x} + e^{7 x} \cdot 7 x

Simplify

= e^{7 x} + 7 e^{7 x} x

\int (2 x + 1) d x

\frac{d}{d x} (3 x^{2} sin (4 x))

\frac{d}{d x} (x^{- 2 c o s (x)})

x \to 0 lim (\frac{( e ^{x} - e ^{- x} - 2 x )}{1 - sin ( x )})

x \to \infty lim (x \cdot π)

What is the derivative of xe^{7x} ?
The derivative of xe^{7x} is e^{7x}+7e^{7x}x
What is the first derivative of xe^{7x} ?
The first derivative of xe^{7x} is e^{7x}+7e^{7x}x