derivative f(x)=ln(100sin^2(x))

Lösung

ableitung von

f (x) = ln (100 sin^{2} (x))

2 cot (x)

Schritte zur Lösung

\frac{d}{d x} (ln (100 sin^{2} (x)))

Wende die Kettenregel an:

\frac{1}{100 sin ^{2} ( x )} \frac{d}{d x} (100 sin^{2} (x))

= \frac{1}{100 sin ^{2} ( x )} \frac{d}{d x} (100 sin^{2} (x))

\frac{d}{d x} (100 sin^{2} (x)) = 200 sin (x) cos (x)

= \frac{1}{100 sin ^{2} ( x )} \cdot 200 sin (x) cos (x)

Vereinfache

\frac{1}{100 sin ^{2} ( x )} \cdot 200 sin (x) cos (x) : 2 cot (x)

= 2 cot (x)

\frac{d ^{2}}{d x ^{2}} (x^{\frac{8}{9}} + 6 x)

\int sin^{\frac{1}{2}} (2 x) cos^{3} (2 x) d x

\int (6 x + 1) 3 x^{2} + x d x

\frac{\partial}{\partial x} (\frac{1}{x y ^{2} + y x ^{2}})

\int \frac{( 2 + ln ( 7 x ) )}{3 x} d x