What is the derivative of 6xe^{5x} ?

The derivative of 6xe^{5x} is 6(e^{5x}+5e^{5x}x)

What is the first derivative of 6xe^{5x} ?

The first derivative of 6xe^{5x} is 6(e^{5x}+5e^{5x}x)

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derivative of

6 x e^{5 x}

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

Solution steps

\frac{d}{d x} (6 x e^{5 x})

Take the constant out:

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

= 6 \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}

= 6 (\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

= 6 (1 \cdot e^{5 x} + e^{5 x} \cdot 5 x)

Simplify

= 6 (e^{5 x} + 5 e^{5 x} x)

What is the derivative of 6xe^{5x} ?
The derivative of 6xe^{5x} is 6(e^{5x}+5e^{5x}x)
What is the first derivative of 6xe^{5x} ?
The first derivative of 6xe^{5x} is 6(e^{5x}+5e^{5x}x)