What is (\partial)/(\partial x)(18ye^{9x}) ?

The answer to (\partial)/(\partial x)(18ye^{9x}) is 162e^{9x}y

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(\partial)/(\partial x)(18ye^{9x})

\frac{\partial}{\partial x} (18 y e^{9 x})

162 e^{9 x} y

Solution steps

\frac{\partial}{\partial x} (18 y e^{9 x})

Treat

y

as a constant

Take the constant out:

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

= 18 y \frac{\partial}{\partial x} (e^{9 x})

Apply the chain rule:

e^{9 x} \frac{\partial}{\partial x} (9 x)

= e^{9 x} \frac{\partial}{\partial x} (9 x)

\frac{\partial}{\partial x} (9 x) = 9

= 18 y e^{9 x} \cdot 9

Simplify

= 162 e^{9 x} y

\int (x - 9) sin (π x) d x

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

f (x) = 5 sin (x)

\frac{d}{d x} (\frac{x ^{2} + 5 x}{x + 2})

y^{^{''}} - 4 y^{^{'}} + y = 0

What is (\partial)/(\partial x)(18ye^{9x}) ?
The answer to (\partial)/(\partial x)(18ye^{9x}) is 162e^{9x}y