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

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

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

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

- sin (x + y^{3})

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (x + y^{3}) = 1

= - sin (x + y^{3}) \cdot 1

Simplify

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

t e^{- 3 t} cos (3 t)

\frac{d}{d x} (\frac{80 - x}{4})

\int \frac{7 x ^{3} - x ^{2} + 8 x + 12}{x ^{4} + 4 x ^{2}} d x

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

\frac{d}{d x} (sin^{2} (x^{3} + 4 x^{2} - 3))

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