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

The answer to (\partial)/(\partial z)(4xy^3(z^2+1)^3) is 24xy^3z(z^2+1)^2

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

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

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

Solution steps

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

Treat

x, y

as constants

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial z} (z^{2} + 1) = 2 z

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

Simplify

= 24 x y^{3} z (z^{2} + 1)^{2}

y = e^{x + 4} + 6

\int e^{iπ z} d z

x \to \infty lim (- 4 + \frac{3}{x})

x (x - 4)

n = 6 \sum \infty e^{5 - 6 n}

What is (\partial)/(\partial z)(4xy^3(z^2+1)^3) ?
The answer to (\partial)/(\partial z)(4xy^3(z^2+1)^3) is 24xy^3z(z^2+1)^2