What is (\partial)/(\partial y)(-x-sin(y^2)) ?

The answer to (\partial)/(\partial y)(-x-sin(y^2)) is -2ycos(y^2)

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(\partial)/(\partial y)(-x-sin(y^2))

\frac{\partial}{\partial y} (- x - sin (y^{2}))

- 2 y cos (y^{2})

Solution steps

\frac{\partial}{\partial y} (- x - sin (y^{2}))

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= - \frac{\partial}{\partial y} (x) - \frac{\partial}{\partial y} (sin (y^{2}))

\frac{\partial}{\partial y} (x) = 0

\frac{\partial}{\partial y} (sin (y^{2})) = cos (y^{2}) \cdot 2 y

= - 0 - cos (y^{2}) \cdot 2 y

Simplify

= - 2 y cos (y^{2})

\int x^{3} (x - 1)^{- 4} d x

\frac{s ^{4}}{s}

f (x) = 3 x^{2} + 3 x + 4

- x^{2} + 6 x

\frac{d}{d x} (\frac{8}{1 + x})

What is (\partial)/(\partial y)(-x-sin(y^2)) ?
The answer to (\partial)/(\partial y)(-x-sin(y^2)) is -2ycos(y^2)