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Beliebt Rechnen >

derivative of ln(cosh(3x))

Lösung

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

Lösung

3 tanh (3 x)

Schritte zur Lösung

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

Wende die Kettenregel an:

\frac{1}{cosh ( 3 x )} \frac{d}{d x} (cosh (3 x))

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

\frac{d}{d x} (cosh (3 x)) = sinh (3 x) \cdot 3

= \frac{1}{cosh ( 3 x )} sinh (3 x) \cdot 3

Vereinfache

\frac{1}{cosh ( 3 x )} sinh (3 x) \cdot 3 : 3 tanh (3 x)

= 3 tanh (3 x)

Graph

Beliebte Beispiele

limit as x approaches pi/4 of (sin(2x)-1)/(4x-pi)

x \to \frac{π}{4} lim (\frac{sin ( 2 x ) - 1}{4 x - π})

derivative of cos(2x+3y)

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

y^{''}-16y^'+63y=240e^x

y^{^{''}} - 16 y^{^{'}} + 63 y = 240 e^{x}

integral of (x-5)/(x^2+2x-3)

\int \frac{x - 5}{x ^{2} + 2 x - 3} d x

tangent f(x)= 3/(5x+2),\at x=-1

t an g e n t f (x) = \frac{3}{5 x + 2}, at x = - 1