What is the d/(dv)(ln(ucos(v))) ?

The d/(dv)(ln(ucos(v))) is -(sin(v))/(cos(v))

What is the first d/(dv)(ln(ucos(v))) ?

The first d/(dv)(ln(ucos(v))) is -(sin(v))/(cos(v))

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\frac{d}{d v} (ln (u cos (v)))

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

Solution steps

\frac{d}{d v} (ln (u cos (v)))

Treat

u

as a constant

Apply the chain rule:

\frac{1}{u cos ( v )} \frac{d}{d v} (u cos (v))

= \frac{1}{u cos ( v )} \frac{d}{d v} (u cos (v))

\frac{d}{d v} (u cos (v)) = - u sin (v)

= \frac{1}{u cos ( v )} (- u sin (v))

Simplify

\frac{1}{u cos ( v )} (- u sin (v)) : - \frac{sin ( v )}{cos ( v )}

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

What is the d/(dv)(ln(ucos(v))) ?
The d/(dv)(ln(ucos(v))) is -(sin(v))/(cos(v))
What is the first d/(dv)(ln(ucos(v))) ?
The first d/(dv)(ln(ucos(v))) is -(sin(v))/(cos(v))