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

The answer to (\partial)/(\partial x)(-x-sin(y^2)) is -1

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

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

- 1

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (sin (y^{2})) = 0

= - 1 - 0

Simplify

= - 1

\int x (cos (x) - sin (x)) d x

\frac{d}{d x} (x - 0.8 - 0.2 \cdot sin (x))

\frac{d}{d x} (- \frac{( 2 x ^{2} + 1 )}{( 1 - x ^{2} ) ^{\frac{5}{2}}})

x \frac{d y}{d x} = y^{2}

sin (4 x)

What is (\partial)/(\partial x)(-x-sin(y^2)) ?
The answer to (\partial)/(\partial x)(-x-sin(y^2)) is -1