d/(dt)((tan(t))/(cos(t)-4))

Lösung

\frac{d}{d t} (\frac{tan ( t )}{cos ( t ) - 4})

\frac{sec ^{2} ( t ) ( cos ( t ) - 4 ) + sin ( t ) tan ( t )}{( cos ( t ) - 4 ) ^{2}}

Schritte zur Lösung

\frac{d}{d t} (\frac{tan ( t )}{cos ( t ) - 4})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d t} ( tan ( t ) ) ( cos ( t ) - 4 ) - \frac{d}{d t} ( cos ( t ) - 4 ) tan ( t )}{( cos ( t ) - 4 ) ^{2}}

\frac{d}{d t} (tan (t)) = sec^{2} (t)

\frac{d}{d t} (cos (t) - 4) = - sin (t)

= \frac{sec ^{2} ( t ) ( cos ( t ) - 4 ) - ( - sin ( t ) ) tan ( t )}{( cos ( t ) - 4 ) ^{2}}

Vereinfache

= \frac{sec ^{2} ( t ) ( cos ( t ) - 4 ) + sin ( t ) tan ( t )}{( cos ( t ) - 4 ) ^{2}}

\int_{0}^{\frac{π}{2}} 20 cos^{5} (x) d x

\frac{d}{d x} (2 x^{3} - 3 x^{2} - 12 x + 5)

d er i v a t i v e y = \frac{cos ( x )}{x ^{5}}

d er i v a t i v e U (x) = - 0.04 x^{2} + 240 x - 10000

y^{^{'}} = t - t y