What is the derivative of-xe^{2x} ?

The derivative of-xe^{2x} is -e^{2x}-2e^{2x}x

What is the first derivative of-xe^{2x} ?

The first derivative of-xe^{2x} is -e^{2x}-2e^{2x}x

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

- e^{2 x} - 2 e^{2 x} x

Solution steps

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

Take the constant out:

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

= - \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}

= - (\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

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

Simplify

- (1 \cdot e^{2 x} + e^{2 x} \cdot 2 x) : - e^{2 x} - 2 e^{2 x} x

= - e^{2 x} - 2 e^{2 x} x

x \cdot y^{2} \cdot \frac{d y}{d x} = y^{3} - 4 \cdot x^{3}, y (1) = 2

x^{2} - 8, 7 x

x \to 0 lim (\frac{sin ( 5 x )}{5})

y^{^{''}} - 2 y^{^{'}} - 8 y = x e^{x} + 4

x \to \frac{π}{2} - lim (cos (x))

What is the derivative of-xe^{2x} ?
The derivative of-xe^{2x} is -e^{2x}-2e^{2x}x
What is the first derivative of-xe^{2x} ?
The first derivative of-xe^{2x} is -e^{2x}-2e^{2x}x