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

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

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

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

ln (z) e^{x y} y

Solution steps

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

Treat

y, z

as constants

Take the constant out:

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

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

\int t^{2} cos (t^{3}) d t

x \to 0 lim (\frac{∣ x ∣}{x} - 1)

\frac{d}{d x} (\frac{3}{1 + x})

y^{^{'}} - 2 y = x y^{3}, y (0) = 22

(x \cdot y) d x + x d y = 0

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