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

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

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

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

12 y (z + 1)^{2}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

\int \frac{2 - x}{x ^{2} + 5 x} d x

x \to 0 lim (- \frac{9}{1 - 9 x})

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

\frac{\partial}{\partial y} (5 x^{2} y)

\frac{d}{d x} (\frac{x ^{2} - 4 x + 20}{x ^{2} + 6 x + 8})

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