What is (\partial)/(\partial x)(yln(xy^2z^3)) ?

The answer to (\partial)/(\partial x)(yln(xy^2z^3)) is y/x

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(\partial)/(\partial x)(yln(xy^2z^3))

\frac{\partial}{\partial x} (y ln (x y^{2} z^{3}))

\frac{y}{x}

Solution steps

\frac{\partial}{\partial x} (y ln (x y^{2} z^{3}))

Treat

y, z

as constants

Take the constant out:

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

= y \frac{\partial}{\partial x} (ln (x y^{2} z^{3}))

Apply the chain rule:

\frac{1}{x y ^{2} z ^{3}} \frac{\partial}{\partial x} (x y^{2} z^{3})

= \frac{1}{x y ^{2} z ^{3}} \frac{\partial}{\partial x} (x y^{2} z^{3})

\frac{\partial}{\partial x} (x y^{2} z^{3}) = y^{2} z^{3}

= y \frac{1}{x y ^{2} z ^{3}} y^{2} z^{3}

Simplify

y \frac{1}{x y ^{2} z ^{3}} y^{2} z^{3} : \frac{y}{x}

= \frac{y}{x}

\int (1)^{2} d x

y^{^{'}} = 3 cos (t) - 2 y, y (0) = 0

y^{^{'}} + 9 y = t + e - 8 t

\frac{d}{d x} (x,)

n = 8 \sum \infty e^{7 - 6 n}

What is (\partial)/(\partial x)(yln(xy^2z^3)) ?
The answer to (\partial)/(\partial x)(yln(xy^2z^3)) is y/x