What is the derivative of 5xe^{5x} ?

The derivative of 5xe^{5x} is 5(e^{5x}+5e^{5x}x)

What is the first derivative of 5xe^{5x} ?

The first derivative of 5xe^{5x} is 5(e^{5x}+5e^{5x}x)

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\frac{d}{d x} (5 x e^{5 x})

5 (e^{5 x} + 5 e^{5 x} x)

Solution steps

\frac{d}{d x} (5 x e^{5 x})

Take the constant out:

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

= 5 \frac{d}{d x} (x e^{5 x})

Apply the Product Rule:

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

f = x, g = e^{5 x}

= 5 (\frac{d x}{d x} e^{5 x} + \frac{d}{d x} (e^{5 x}) x)

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

\frac{d}{d x} (e^{5 x}) = e^{5 x} \cdot 5

= 5 (1 \cdot e^{5 x} + e^{5 x} \cdot 5 x)

Simplify

= 5 (e^{5 x} + 5 e^{5 x} x)

x \to - 3 lim (\frac{x}{x - 4})

\int 2 e^{x} - 1 d x

\int 4 x + 1 d x

x \to 0 lim (\frac{6 x ^{2}}{2 x ^{2}})

\int 3 2 x^{2} d x

What is the derivative of 5xe^{5x} ?
The derivative of 5xe^{5x} is 5(e^{5x}+5e^{5x}x)
What is the first derivative of 5xe^{5x} ?
The first derivative of 5xe^{5x} is 5(e^{5x}+5e^{5x}x)