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

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

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

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)

\frac{d}{d t} (- \frac{1}{t ^{2}})

x \to 2 lim (4 - x^{2})

\frac{d}{d x} ((A x^{2} + B x + C) e^{x})

\frac{d}{d x} (3 x - 4)

x \to \infty lim (\frac{e ^{3 x - 8}}{5 x})

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