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

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

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

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

ln (y) e^{x y} y

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

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

8 x^{3}

x \to 3 lim (\frac{2 x + 3}{x - 2})

\frac{d y}{d x} - 2 x y = - 15 x^{2} e^{x^{2}}

f (x) = 6 x^{4} + 7 x - 8, (1, 5)

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