What is (\partial)/(\partial y)(x^2z^2sin(4y)) ?

The answer to (\partial)/(\partial y)(x^2z^2sin(4y)) is x^2z^2cos(4y)*4

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(\partial)/(\partial y)(x^2z^2sin(4y))

\frac{\partial}{\partial y} (x^{2} z^{2} sin (4 y))

x^{2} z^{2} cos (4 y) \cdot 4

Solution steps

\frac{\partial}{\partial y} (x^{2} z^{2} sin (4 y))

Treat

x, z

as constants

Take the constant out:

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

= x^{2} z^{2} \frac{\partial}{\partial y} (sin (4 y))

Apply the chain rule:

cos (4 y) \frac{\partial}{\partial y} (4 y)

= cos (4 y) \frac{\partial}{\partial y} (4 y)

\frac{\partial}{\partial y} (4 y) = 4

= x^{2} z^{2} cos (4 y) \cdot 4

\int (x cos (3 x)) d x

x \to - 2 lim (\frac{2 x ^{3} + 9 x ^{2} + 12 x + 4}{- x ^{3} - 2 x ^{2} + 4 x + 8})

\int - x^{\frac{3}{2}} d x

\int_{- 1}^{1} (x^{3} - x) d x

\int_{0}^{c} 9 e^{3 x} d x

What is (\partial)/(\partial y)(x^2z^2sin(4y)) ?
The answer to (\partial)/(\partial y)(x^2z^2sin(4y)) is x^2z^2cos(4y)*4