What is (\partial)/(\partial y)(-10ysin(xy)) ?

The answer to (\partial)/(\partial y)(-10ysin(xy)) is -10(sin(yx)+yxcos(yx))

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(\partial)/(\partial y)(-10ysin(xy))

\frac{\partial}{\partial y} (- 10 y sin (x y))

- 10 (sin (y x) + y x cos (y x))

Solution steps

\frac{\partial}{\partial y} (- 10 y sin (x y))

Treat

x

as a constant

Take the constant out:

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

= - 10 \frac{\partial}{\partial y} (y sin (x y))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = sin (x y)

= - 10 (\frac{\partial}{\partial y} (y) sin (x y) + \frac{\partial}{\partial y} (sin (x y)) y)

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

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

= - 10 (1 \cdot sin (x y) + cos (x y) x y)

Simplify

= - 10 (sin (y x) + y x cos (y x))

y = x^{x^{2}}

\frac{\partial}{\partial x} (- x cos (y))

\int 3 cos (x) - \frac{1}{x} d x

\int_{1}^{11} \frac{1}{x - 8} d x

\int_{- 2}^{2} \frac{10}{x ^{2} - 4 x - 21} d x

What is (\partial)/(\partial y)(-10ysin(xy)) ?
The answer to (\partial)/(\partial y)(-10ysin(xy)) is -10(sin(yx)+yxcos(yx))