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

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

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(\partial)/(\partial x)(-y(y+sin(x)))

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

- y cos (x)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (sin (x)) = cos (x)

= - y (0 + cos (x))

Simplify

= - y cos (x)

1 - \frac{3 x}{x ^{3} + 27}

\int \frac{1}{x ^{2} + 12 x + 35} d x

(- 4.4) (- 1.5)

\frac{d}{d x} (\frac{9}{sin ( x ) + cos ( x )})

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