What is (\partial)/(\partial x)(x^ay^bz^c) ?

The answer to (\partial)/(\partial x)(x^ay^bz^c) is y^bz^cax^{a-1}

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(\partial)/(\partial x)(x^ay^bz^c)

\frac{\partial}{\partial x} (x^{a} y^{b} z^{c})

y^{b} z^{c} a x^{a - 1}

Solution steps

\frac{\partial}{\partial x} (x^{a} y^{b} z^{c})

Treat

a, y, b, z, c

as constants

Take the constant out:

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

= y^{b} z^{c} \frac{\partial}{\partial x} (x^{a})

Apply the Power Rule:

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

= y^{b} z^{c} a x^{a - 1}

y = (\frac{1}{2 x + 1} - 2)^{3}

\frac{d}{d x} (ln (e^{7 x}))

x \to - 3 lim (- 1)

\int \frac{1}{( x + 4 ) x ^{2} + 8 x} d x

b e^{x}

What is (\partial)/(\partial x)(x^ay^bz^c) ?
The answer to (\partial)/(\partial x)(x^ay^bz^c) is y^bz^cax^{a-1}