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

The answer to (\partial)/(\partial z)(4y(z+1)^2) is 8y(z+1)

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

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

8 y (z + 1)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= 4 y \cdot 2 (z + 1) \cdot 1

Simplify

= 8 y (z + 1)

\int (10 x) d x

\frac{d}{d x} (\frac{2 x ^{2} + 6 x + 2}{x})

x \to 3 - lim (k (x) (x - 5))

\frac{\partial}{\partial z} (e^{x y} + ln (2 x z) + sin (x^{2} y^{2}))

\frac{d}{d x} (\frac{x g ( x ) ( x ) ^{x - 1}}{x ^{2} + 1})

What is (\partial)/(\partial z)(4y(z+1)^2) ?
The answer to (\partial)/(\partial z)(4y(z+1)^2) is 8y(z+1)