derivative of (csc(xtan(x))/(cos(x)))

Lösung

\frac{d}{d x} (\frac{csc ( x ) tan ( x )}{cos ( x )})

2 sec^{2} (x) tan (x)

Schritte zur Lösung

\frac{d}{d x} (\frac{csc ( x ) tan ( x )}{cos ( x )})

Vereinfache

\frac{csc ( x ) tan ( x )}{cos ( x )} : sec^{2} (x)

= \frac{d}{d x} (sec^{2} (x))

Wende die Kettenregel an:

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

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

\frac{d}{d x} (sec (x)) = sec (x) tan (x)

= 2 sec (x) sec (x) tan (x)

Vereinfache

2 sec (x) sec (x) tan (x) : 2 sec^{2} (x) tan (x)

= 2 sec^{2} (x) tan (x)

x \to 5 lim (5 x - 4)

\int \frac{x ^{4} + x - 9}{x ^{2} + 3} d x

\frac{\partial}{\partial x} (x^{3} + y^{3} + z^{3} + 6 x yz)

\int \frac{3 - 4 x ^{3} + 6 x ^{6}}{x ^{6}} d x

- y^{^{'''}} + 2 y^{^{''}} + 3 y^{^{'}} + 3 = 0