derivative of 1/2 ln^2(x)

الحلّ

\frac{d}{d x} (\frac{1}{2} ln^{2} (x))

\frac{ln ( x )}{x}

خطوات الحلّ

\frac{d}{d x} (\frac{1}{2} ln^{2} (x))

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

:استخرج الثابت

= \frac{1}{2} \frac{d}{d x} (ln^{2} (x))

استعمل قانون السلسلة:

2 ln (x) \frac{d}{d x} (ln (x))

= 2 ln (x) \frac{d}{d x} (ln (x))

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

= \frac{1}{2} \cdot 2 ln (x) \frac{1}{x}

\frac{1}{2} \cdot 2 ln (x) \frac{1}{x}

بسّط:

\frac{ln ( x )}{x}

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

- 7 csc (5 x) e^{3 x}

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

\int_{0}^{4} x^{2} - 9 d x

\frac{3}{2 s + 1}

f (x) = 14 - e^{x}