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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

e^{- \frac{x}{2}}

\frac{d}{d x} (\frac{x + 3}{x + 1})

\int 7 - 4 x - 4 x^{2} d x

\int (a + 18)^{2} d a

\int sin (x + n x) d x

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