What is the first (ln(sin(x)))^' ?

The first (ln(sin(x)))^' is cot(x)

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(ln(sin(x)))^'

(ln (sin (x)))^{^{'}}

cot (x)

Solution steps

(ln (sin (x)))^{'}

Apply the chain rule:

\frac{1}{sin ( x )} (sin (x))^{'}

= \frac{1}{sin ( x )} (sin (x))^{'}

(sin (x))^{'} = cos (x)

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

Simplify

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

= cot (x)

\frac{\partial}{\partial x} ((1 x, 3 y, 4 z) \cdot (1, 2, 3))

\int_{3}^{6} (3 x - x)^{2} d x

\int (x^{20} - 5 x^{4})^{3} (x^{19} - x^{3}) d x

f (x) = \frac{6}{x}, at x = 4

f (x) = cos (a^{7} + x^{7})