derivative-ln(cos(x))

الحلّ

derivative of

- ln (cos (x))

tan (x)

خطوات الحلّ

\frac{d}{d x} (- ln (cos (x)))

(a \cdot f)^{'} = a \cdot f^{'}

:استخرج الثابت

= - \frac{d}{d x} (ln (cos (x)))

استعمل قانون السلسلة:

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

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

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

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

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

بسّط:

tan (x)

= tan (x)

\int x^{5} x^{3} - 1 d x

x \to 0 lim (\frac{arctan ( x ) - x}{8 x ^{3}})

\int 2 (sin (x) - cos (x) + x) d x

x \to - 2 lim (x^{2} - 3 x + 5)

\int_{2}^{x} 1 + t^{2} d t