What is (\partial)/(\partial x)(3ye^{5x}) ?

The answer to (\partial)/(\partial x)(3ye^{5x}) is 15e^{5x}y

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(\partial)/(\partial x)(3ye^{5x})

\frac{\partial}{\partial x} (3 y e^{5 x})

15 e^{5 x} y

Solution steps

\frac{\partial}{\partial x} (3 y e^{5 x})

Treat

y

as a constant

Take the constant out:

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

= 3 y \frac{\partial}{\partial x} (e^{5 x})

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (5 x) = 5

= 3 y e^{5 x} \cdot 5

Simplify

= 15 e^{5 x} y

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What is (\partial)/(\partial x)(3ye^{5x}) ?
The answer to (\partial)/(\partial x)(3ye^{5x}) is 15e^{5x}y