What is (\partial)/(\partial x)(y^4cos(6x)) ?

The answer to (\partial)/(\partial x)(y^4cos(6x)) is -6y^4sin(6x)

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(\partial)/(\partial x)(y^4cos(6x))

\frac{\partial}{\partial x} (y^{4} cos (6 x))

- 6 y^{4} sin (6 x)

Solution steps

\frac{\partial}{\partial x} (y^{4} cos (6 x))

Treat

y

as a constant

Take the constant out:

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

= y^{4} \frac{\partial}{\partial x} (cos (6 x))

Apply the chain rule:

- sin (6 x) \frac{\partial}{\partial x} (6 x)

= - sin (6 x) \frac{\partial}{\partial x} (6 x)

\frac{\partial}{\partial x} (6 x) = 6

= y^{4} (- sin (6 x) \cdot 6)

Simplify

= - 6 y^{4} sin (6 x)

\int \frac{x ^{2}}{x ^{2} + x + 2} d x

\int \frac{e ^{x}}{4 - 9 e ^{2 x}} d x

\frac{\partial}{\partial x} (5 - x^{4} + 2 x^{2} - y^{2})

(cos (9 x))^{x}

48 y^{^{''}} + 34 y^{^{'}} - 5 y = 0

What is (\partial)/(\partial x)(y^4cos(6x)) ?
The answer to (\partial)/(\partial x)(y^4cos(6x)) is -6y^4sin(6x)