What is (\partial)/(\partial z)(6y(z+1)^4) ?

The answer to (\partial)/(\partial z)(6y(z+1)^4) is 24y(z+1)^3

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(\partial)/(\partial z)(6y(z+1)^4)

\frac{\partial}{\partial z} (6 y (z + 1)^{4})

24 y (z + 1)^{3}

Solution steps

\frac{\partial}{\partial z} (6 y (z + 1)^{4})

Treat

y

as a constant

Take the constant out:

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

= 6 y \frac{\partial}{\partial z} ((z + 1)^{4})

Apply the chain rule:

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

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

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

= 6 y \cdot 4 (z + 1)^{3} \cdot 1

Simplify

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

\int (1 - 2 x) d x

x \to - \infty lim (1 x)

y = x^{2} + 1, y = 5

f (x) = 7 x^{2} - x^{3}, (1, 6)

\int 18 x^{2} - 14 x + 9 d x

What is (\partial)/(\partial z)(6y(z+1)^4) ?
The answer to (\partial)/(\partial z)(6y(z+1)^4) is 24y(z+1)^3