What is (\partial)/(\partial x)(x^4ln(zy)) ?

The answer to (\partial)/(\partial x)(x^4ln(zy)) is 4x^3ln(zy)

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(\partial)/(\partial x)(x^4ln(zy))

\frac{\partial}{\partial x} (x^{4} ln (zy))

4 x^{3} ln (zy)

Solution steps

\frac{\partial}{\partial x} (x^{4} ln (zy))

Treat

z, y

as constants

Take the constant out:

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

= ln (zy) \frac{\partial}{\partial x} (x^{4})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= ln (zy) \cdot 4 x^{4 - 1}

Simplify

= 4 x^{3} ln (zy)

\frac{d}{d x} (\frac{e ^{x}}{x ^{n}})

\frac{d}{d x} (3 1 - 2 x)

\int \frac{7}{25 - x ^{2}} d x

2 x y

y^{^{'}} = y + sin (x) - cos (x)

What is (\partial)/(\partial x)(x^4ln(zy)) ?
The answer to (\partial)/(\partial x)(x^4ln(zy)) is 4x^3ln(zy)