derivative sin(x)ln(3x)

Lösung

ableitung von

sin (x) ln (3 x)

cos (x) ln (3 x) + \frac{sin ( x )}{x}

Schritte zur Lösung

\frac{d}{d x} (sin (x) ln (3 x))

Wende die Produktregel an:

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

f = sin (x), g = ln (3 x)

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

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

\frac{d}{d x} (ln (3 x)) = \frac{1}{x}

= cos (x) ln (3 x) + \frac{1}{x} sin (x)

\frac{1}{x} sin (x) = \frac{sin ( x )}{x}

= cos (x) ln (3 x) + \frac{sin ( x )}{x}

t an g e n t f (x) = - 2 x^{5} + 11 x^{3}, at x = - 2

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

\int_{2}^{\infty} \frac{1}{e ^{x}} d x

t \to - 2 lim (\frac{t + 2}{t ^{2} - 4})

x \frac{d y}{d x} + 10 y = 9 y^{2}, y (1) = - 1