What is (\partial)/(\partial x)(y^3cos(6x)) ?

The answer to (\partial)/(\partial x)(y^3cos(6x)) is -6y^3sin(6x)

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(\partial)/(\partial x)(y^3cos(6x))

\frac{\partial}{\partial x} (y^{3} cos (6 x))

- 6 y^{3} sin (6 x)

Solution steps

\frac{\partial}{\partial x} (y^{3} cos (6 x))

Treat

y

as a constant

Take the constant out:

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

= y^{3} \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^{3} (- sin (6 x) \cdot 6)

Simplify

= - 6 y^{3} sin (6 x)

y^{^{''}} - y^{^{'}} = sin (x)

\int_{1}^{3} 2 x d x

\int 2 x y^{3} d x

\int x^{2} cos (3 x) d x

\int \frac{r ^{3}}{16 + r ^{2}} d r

What is (\partial)/(\partial x)(y^3cos(6x)) ?
The answer to (\partial)/(\partial x)(y^3cos(6x)) is -6y^3sin(6x)