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

The answer to (\partial)/(\partial z)(x^ay^bz^c) is x^ay^bcz^{c-1}

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

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

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

Solution steps

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

Treat

a, x, y, b, c

as constants

Take the constant out:

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

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

Apply the Power Rule:

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

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

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

y^{^{'}} + \frac{y}{x} = 7 x^{3} y^{2}

3^{x}

\frac{d}{d x} (e^{3 x} sin (x))

\int x^{2} (1 - x^{3})^{4} d x

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