derivative of arccos(sin(x^2+9x))

Lösung

\frac{d}{d x} (arccos (sin (x^{2} + 9 x)))

- 2 x - 9

Schritte zur Lösung

\frac{d}{d x} (arccos (sin (x^{2} + 9 x)))

Wende die Kettenregel an:

- \frac{1}{1 - ( sin ( x ^{2} + 9 x ) ) ^{2}} \frac{d}{d x} (sin (x^{2} + 9 x))

= - \frac{1}{1 - ( sin ( x ^{2} + 9 x ) ) ^{2}} \frac{d}{d x} (sin (x^{2} + 9 x))

\frac{d}{d x} (sin (x^{2} + 9 x)) = cos (x^{2} + 9 x) (2 x + 9)

= - \frac{1}{1 - ( sin ( x ^{2} + 9 x ) ) ^{2}} cos (x^{2} + 9 x) (2 x + 9)

Vereinfache

- \frac{1}{1 - sin ^{2} ( x ^{2} + 9 x )} cos (x^{2} + 9 x) (2 x + 9) : - 2 x - 9

= - 2 x - 9

d er i v a t i v e f (x) = 3 x + 4

t an g e n t f (x) = \frac{2}{4 - x}, at x = 1

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

im pl i c i t 7 x^{2} - y^{2} = 4

a re a y = x^{3}, y = 8, x = - 1