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

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

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(\partial)/(\partial x)(-yln(y)sin(xln(y)))

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

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

Solution steps

\frac{\partial}{\partial x} (- y ln (y) sin (x 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 - 1 lim (x^{2} - 2 ln (x))

\frac{\partial}{\partial x} (4 z - 18 x y)

\int \frac{1 + cos ( 7 x )}{6} d x

y^{\frac{1}{2}} \frac{d y}{d x} + y^{\frac{3}{2}} = 1

\frac{\partial}{\partial x} (\frac{x ^{2}}{1 + t ^{2}})

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