What is (\partial)/(\partial y)(4xy^3(z^2+1)^3) ?

The answer to (\partial)/(\partial y)(4xy^3(z^2+1)^3) is 12xy^2(z^2+1)^3

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(\partial)/(\partial y)(4xy^3(z^2+1)^3)

\frac{\partial}{\partial y} (4 x y^{3} (z^{2} + 1)^{3})

12 x y^{2} (z^{2} + 1)^{3}

Solution steps

\frac{\partial}{\partial y} (4 x y^{3} (z^{2} + 1)^{3})

Treat

x, z

as constants

Take the constant out:

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

= 4 x (z^{2} + 1)^{3} \frac{\partial}{\partial y} (y^{3})

Apply the Power Rule:

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

= 4 x (z^{2} + 1)^{3} \cdot 3 y^{3 - 1}

Simplify

= 12 x y^{2} (z^{2} + 1)^{3}

f (x) = \frac{e ^{3 x}}{x ^{15}}

x \to + 2 - lim (x - 2)

\int \frac{e ^{u}}{( 8 - e ^{u} ) ^{2}} d u

(1 + 5 x^{2}) (x - x^{2})

\frac{d x}{d t} = 2 x^{2} - 3 x

What is (\partial)/(\partial y)(4xy^3(z^2+1)^3) ?
The answer to (\partial)/(\partial y)(4xy^3(z^2+1)^3) is 12xy^2(z^2+1)^3