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

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

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(\partial)/(\partial y)(x^2cos(4y))

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

- 4 x^{2} sin (4 y)

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

- sin (4 y) \frac{\partial}{\partial y} (4 y)

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

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

= x^{2} (- sin (4 y) \cdot 4)

Simplify

= - 4 x^{2} sin (4 y)

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