What is (\partial)/(\partial x)(y^5cos(4x)) ?

The answer to (\partial)/(\partial x)(y^5cos(4x)) is -4y^5sin(4x)

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(\partial)/(\partial x)(y^5cos(4x))

\frac{\partial}{\partial x} (y^{5} cos (4 x))

- 4 y^{5} sin (4 x)

Solution steps

\frac{\partial}{\partial x} (y^{5} cos (4 x))

Treat

y

as a constant

Take the constant out:

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

= y^{5} \frac{\partial}{\partial x} (cos (4 x))

Apply the chain rule:

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

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

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

= y^{5} (- sin (4 x) \cdot 4)

Simplify

= - 4 y^{5} sin (4 x)

What is (\partial)/(\partial x)(y^5cos(4x)) ?
The answer to (\partial)/(\partial x)(y^5cos(4x)) is -4y^5sin(4x)