derivative g(x)=3arccos(x/2)

פתרון

derivative of

g (x) = 3 arccos (\frac{x}{2})

- \frac{3}{4 - x ^{2}}

צעדי פתרון

\frac{d}{d x} (3 arccos (\frac{x}{2}))

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

:הוצא את הקבוע

= 3 \frac{d}{d x} (arccos (\frac{x}{2}))

השתמש בחוק השרשרת:

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

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

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

= 3 - \frac{1}{1 - ( \frac{x}{2} ) ^{2}} \cdot \frac{1}{2}

3 - \frac{1}{1 - ( \frac{x}{2} ) ^{2}} \cdot \frac{1}{2}

פשט את:

- \frac{3}{4 - x ^{2}}

= - \frac{3}{4 - x ^{2}}

n = 1 \sum \infty \frac{4 ^{n}}{n + 1}

n = 1 \sum \infty \frac{1}{n ( n + 8 )}

168 (2 x + 5)^{5}

\frac{d}{d x} (lo g_{7} (x^{2} - 7))

f (x) = 4 x^{4} - 3 x^{\frac{5}{2}} + 2