What is the derivative of xe^{6x} ?

The derivative of xe^{6x} is e^{6x}+6e^{6x}x

What is the first derivative of xe^{6x} ?

The first derivative of xe^{6x} is e^{6x}+6e^{6x}x

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\frac{d}{d x} (x e^{6 x})

e^{6 x} + 6 e^{6 x} x

Solution steps

\frac{d}{d x} (x e^{6 x})

Apply the Product Rule:

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

f = x, g = e^{6 x}

= \frac{d x}{d x} e^{6 x} + \frac{d}{d x} (e^{6 x}) x

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

\frac{d}{d x} (e^{6 x}) = e^{6 x} \cdot 6

= 1 \cdot e^{6 x} + e^{6 x} \cdot 6 x

Simplify

= e^{6 x} + 6 e^{6 x} x

- \frac{x ^{2}}{4} + \frac{22}{4}

f (x) = x^{2} + 5, (1, 6)

\frac{\partial}{\partial x} (y + x)

(2 x + 5)^{7}

\frac{\partial}{\partial x} (4 x^{2} - 2 y^{2})

What is the derivative of xe^{6x} ?
The derivative of xe^{6x} is e^{6x}+6e^{6x}x
What is the first derivative of xe^{6x} ?
The first derivative of xe^{6x} is e^{6x}+6e^{6x}x