What is (\partial)/(\partial x)(ln(cos(xy)+2)) ?

The answer to (\partial)/(\partial x)(ln(cos(xy)+2)) is -(ysin(xy))/(cos(xy)+2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(ln(cos(xy)+2))

\frac{\partial}{\partial x} (ln (cos (x y) + 2))

- \frac{y sin ( x y )}{cos ( x y ) + 2}

Solution steps

\frac{\partial}{\partial x} (ln (cos (x y) + 2))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{cos ( x y ) + 2} \frac{\partial}{\partial x} (cos (x y) + 2)

= \frac{1}{cos ( x y ) + 2} \frac{\partial}{\partial x} (cos (x y) + 2)

\frac{\partial}{\partial x} (cos (x y) + 2) = - y sin (y x)

= \frac{1}{cos ( x y ) + 2} (- y sin (y x))

Simplify

\frac{1}{cos ( x y ) + 2} (- y sin (y x)) : - \frac{y sin ( x y )}{cos ( x y ) + 2}

= - \frac{y sin ( x y )}{cos ( x y ) + 2}

\int tan^{4} (x) + tan^{6} (x) d x

h \to 0 lim (\frac{1}{5 - h})

\frac{e ^{- 2 s}}{s ( s - 1 )}

\frac{d}{d x} (- 2 x + 2)

\int 13 tan (x) sec^{4} (x) d x

What is (\partial)/(\partial x)(ln(cos(xy)+2)) ?
The answer to (\partial)/(\partial x)(ln(cos(xy)+2)) is -(ysin(xy))/(cos(xy)+2)