What is (\partial)/(\partial x)(e^{xy}ln(9y)) ?

The answer to (\partial)/(\partial x)(e^{xy}ln(9y)) is ln(9y)e^{xy}y

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(\partial)/(\partial x)(e^{xy}ln(9y))

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

ln (9 y) e^{x y} y

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= ln (9 y) e^{x y} y

\frac{d}{d x} (5 - \frac{2}{x})

\int_{3}^{\infty} \frac{ln ( x )}{x} d x

x \to 0 - lim (\frac{∣ x ∣}{x})

f (x) = 4 e^{x} cos (x), (0, 4)

(2 x - 3) e^{3 x}

What is (\partial)/(\partial x)(e^{xy}ln(9y)) ?
The answer to (\partial)/(\partial x)(e^{xy}ln(9y)) is ln(9y)e^{xy}y