What is the derivative of log_{e}(1/(csc(x))) ?

The derivative of log_{e}(1/(csc(x))) is cot(x)

What is the first derivative of log_{e}(1/(csc(x))) ?

The first derivative of log_{e}(1/(csc(x))) is cot(x)

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derivative of

lo g_{e} (\frac{1}{csc ( x )})

cot (x)

Solution steps

\frac{d}{d x} (lo g_{e} (\frac{1}{csc ( x )}))

Simplify

lo g_{e} (\frac{1}{csc ( x )}) : ln (sin (x))

= \frac{d}{d x} (ln (sin (x)))

Apply the chain rule:

\frac{1}{sin ( x )} \frac{d}{d x} (sin (x))

= \frac{1}{sin ( x )} \frac{d}{d x} (sin (x))

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

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

Simplify

\frac{1}{sin ( x )} cos (x) : cot (x)

= cot (x)

(1 + x)^{\frac{1}{x}}

y^{^{'''}} + 10 y^{^{''}} + 25 y^{^{'}} = 0

\frac{\partial}{\partial x} (- 2 x y + x^{3})

f (x) = 2 - 3 x^{2}, at x = - 2

\frac{d y}{d x} = y^{2} - 2 y

What is the derivative of log_{e}(1/(csc(x))) ?
The derivative of log_{e}(1/(csc(x))) is cot(x)
What is the first derivative of log_{e}(1/(csc(x))) ?
The first derivative of log_{e}(1/(csc(x))) is cot(x)