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

The answer to (\partial)/(\partial y)(3xy^2z^2) is 6xyz^2

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(\partial)/(\partial y)(3xy^2z^2)

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

6 x y z^{2}

Solution steps

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

Treat

x, z

as constants

Take the constant out:

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

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

Apply the Power Rule:

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

= 3 x z^{2} \cdot 2 y^{2 - 1}

Simplify

= 6 x y z^{2}

f^{^{'}} (t) = \frac{6}{t ^{6}} - \frac{3}{t ^{3}} + \frac{2}{t}

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

f (y) = sin (y)

x \to 1 lim (e^{2 x})

f (x) = - 4 x^{2} - 4, g (x) = 2 x^{2} - 9

What is (\partial)/(\partial y)(3xy^2z^2) ?
The answer to (\partial)/(\partial y)(3xy^2z^2) is 6xyz^2