derivative of sin(ln(3x^2+x))

Lösung

\frac{d}{d x} (sin (ln (3 x^{2} + x)))

\frac{cos ( ln ( 3 x ^{2} + x ) ) ( 6 x + 1 )}{3 x ^{2} + x}

Schritte zur Lösung

\frac{d}{d x} (sin (ln (3 x^{2} + x)))

Wende die Kettenregel an:

cos (ln (3 x^{2} + x)) \frac{d}{d x} (ln (3 x^{2} + x))

= cos (ln (3 x^{2} + x)) \frac{d}{d x} (ln (3 x^{2} + x))

\frac{d}{d x} (ln (3 x^{2} + x)) = \frac{6 x + 1}{3 x ^{2} + x}

= cos (ln (3 x^{2} + x)) \frac{6 x + 1}{3 x ^{2} + x}

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{cos ( ln ( 3 x ^{2} + x ) ) ( 6 x + 1 )}{3 x ^{2} + x}

\frac{d}{d x} (- \frac{10}{10 - x})

\int \frac{1}{x \cdot 1 - x ^{2}} d x

\frac{d}{d x} (a x e^{2 x})

t an g e n t f (x) = x^{3} + x^{2} + (\frac{6}{x}), at x = 1

t an g e n t y = (x - 4)^{2}, at x = 5