derivative of sin(5xln(sin^2(5x)))

Lösung

\frac{d}{d x} (sin (5 x) ln (sin^{2} (5 x)))

cos (5 x) \cdot 5 ln (sin^{2} (5 x)) + 5 csc^{2} (5 x) sin (10 x) sin (5 x)

Schritte zur Lösung

\frac{d}{d x} (sin (5 x) ln (sin^{2} (5 x)))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sin (5 x), g = ln (sin^{2} (5 x))

= \frac{d}{d x} (sin (5 x)) ln (sin^{2} (5 x)) + \frac{d}{d x} (ln (sin^{2} (5 x))) sin (5 x)

\frac{d}{d x} (sin (5 x)) = cos (5 x) \cdot 5

\frac{d}{d x} (ln (sin^{2} (5 x))) = 5 csc^{2} (5 x) sin (10 x)

= cos (5 x) \cdot 5 ln (sin^{2} (5 x)) + 5 csc^{2} (5 x) sin (10 x) sin (5 x)

in v erse l a pl a ce \frac{10}{s ^{3} + 2 s ^{2} + 20 s}

\int_{0}^{1} 0 d x

\int_{0}^{1} \frac{1}{4 y - 1} d y

d er i v a t i v e f (x) = \frac{6}{x}

x \to 0 lim (\frac{( 2 x ^{2} + 16 )}{x})