derivative of (sec(sin(sqrt(x^2+6^x)))^4)

Lösung

\frac{d}{d x} ((sec (sin (x^{2} + 6^{x})))^{4})

\frac{2 sec ^{4} ( sin ( x ^{2} + 6 ^{x} ) ) cos ( x ^{2} + 6 ^{x} ) tan ( sin ( x ^{2} + 6 ^{x} ) ) ( 2 x + ln ( 6 ) \cdot 6 ^{x} )}{x ^{2} + 6 ^{x}}

Schritte zur Lösung

\frac{d}{d x} ((sec (sin (x^{2} + 6^{x})))^{4})

Wende die Kettenregel an:

4 (sec (sin (x^{2} + 6^{x})))^{3} \frac{d}{d x} (sec (sin (x^{2} + 6^{x})))

= 4 (sec (sin (x^{2} + 6^{x})))^{3} \frac{d}{d x} (sec (sin (x^{2} + 6^{x})))

\frac{d}{d x} (sec (sin (x^{2} + 6^{x}))) = \frac{cos ( x ^{2} + 6 ^{x} ) sec ( sin ( x ^{2} + 6 ^{x} ) ) tan ( sin ( x ^{2} + 6 ^{x} ) ) ( 2 x + ln ( 6 ) \cdot 6 ^{x} )}{2 x ^{2} + 6 ^{x}}

= 4 (sec (sin (x^{2} + 6^{x})))^{3} \frac{cos ( x ^{2} + 6 ^{x} ) sec ( sin ( x ^{2} + 6 ^{x} ) ) tan ( sin ( x ^{2} + 6 ^{x} ) ) ( 2 x + ln ( 6 ) \cdot 6 ^{x} )}{2 x ^{2} + 6 ^{x}}

Vereinfache

4 sec^{3} (sin (x^{2} + 6^{x})) \frac{cos ( x ^{2} + 6 ^{x} ) sec ( sin ( x ^{2} + 6 ^{x} ) ) tan ( sin ( x ^{2} + 6 ^{x} ) ) ( 2 x + ln ( 6 ) \cdot 6 ^{x} )}{2 x ^{2} + 6 ^{x}} : \frac{2 sec ^{4} ( sin ( x ^{2} + 6 ^{x} ) ) cos ( x ^{2} + 6 ^{x} ) tan ( sin ( x ^{2} + 6 ^{x} ) ) ( 2 x + ln ( 6 ) \cdot 6 ^{x} )}{x ^{2} + 6 ^{x}}

= \frac{2 sec ^{4} ( sin ( x ^{2} + 6 ^{x} ) ) cos ( x ^{2} + 6 ^{x} ) tan ( sin ( x ^{2} + 6 ^{x} ) ) ( 2 x + ln ( 6 ) \cdot 6 ^{x} )}{x ^{2} + 6 ^{x}}

\int 9 x^{3} e^{x} d x

\frac{d}{d x} (\frac{x ^{2}}{( 2 + x )})

x (\frac{d y}{d x}) + y = 4 x + 1

d er i v a t i v e x - 4

a re a y = sin (x), y = 3 x, x = \frac{π}{2}, x = π