What is (\partial)/(\partial x)(ycos(xlog_{e}(y))) ?

The answer to (\partial)/(\partial x)(ycos(xlog_{e}(y))) is -ysin(xln(y))ln(y)

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(\partial)/(\partial x)(ycos(xlog_{e}(y)))

\frac{\partial}{\partial x} (y cos (x lo g_{e} (y)))

- y sin (x ln (y)) ln (y)

Solution steps

\frac{\partial}{\partial x} (y cos (x lo g_{e} (y)))

Simplify

y cos (x lo g_{e} (y)) : y cos (x ln (y))

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= y (- sin (x ln (y)) ln (y))

Simplify

= - y sin (x ln (y)) ln (y)

x \to \infty lim (\frac{2}{0})

\frac{d y}{d t} = - 3 (y - 5)

x \to \infty lim (\frac{( \frac{x + 1}{x ^{3} + 2} )}{( \frac{x}{x ^{3}} )})

x \to 5 + lim (\frac{8}{x - 5})

\int sin (ln (2 x)) d x

What is (\partial)/(\partial x)(ycos(xlog_{e}(y))) ?
The answer to (\partial)/(\partial x)(ycos(xlog_{e}(y))) is -ysin(xln(y))ln(y)