What is (\partial)/(\partial x)(ln(ycos(x))) ?

The answer to (\partial)/(\partial x)(ln(ycos(x))) is -(sin(x))/(cos(x))

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(\partial)/(\partial x)(ln(ycos(x)))

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

- \frac{sin ( x )}{cos ( x )}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{sin ( x )}{cos ( x )}

y = e^{x}, at x = ln (2)

\int x (2 x + 5)^{20} d x

\frac{\partial}{\partial x} (7 e^{x} sin (y))

x \to 2 lim (7 x - 4)

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

What is (\partial)/(\partial x)(ln(ycos(x))) ?
The answer to (\partial)/(\partial x)(ln(ycos(x))) is -(sin(x))/(cos(x))