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

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

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

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

\frac{y}{x}

Solution steps

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

Treat

p, y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{y}{x}

x \to 0 + lim (3 (x)^{\frac{x}{2}})

\int_{0}^{7} \frac{1}{49 - x ^{2}} d x

cos (sin (3 x))

\int 3 t^{2} + 6 t d t

\frac{d y}{d x} = 8 x y + 1

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