What is (\partial)/(\partial x)(-ysin(xln(y))ln(y)) ?

The answer to (\partial)/(\partial x)(-ysin(xln(y))ln(y)) is -ycos(xln(y))ln^2(y)

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(\partial)/(\partial x)(-ysin(xln(y))ln(y))

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

- y cos (x ln (y)) ln^{2} (y)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= - y ln (y) cos (x ln (y)) ln (y)

Simplify

- y ln (y) cos (x ln (y)) ln (y) : - y cos (x ln (y)) ln^{2} (y)

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

x \to e lim (- 11 - 12)

y = x + 12

2 x - 1 + (3 y + 7) \frac{d y}{d x} = 0

\int \frac{1}{2 x} - \frac{2}{x ^{2}} + \frac{3}{x} d x

\int \frac{cos ( x )}{1 + sin ( x )} d x

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