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Beliebt Rechnen >

derivative of ln(sinh(5x))

Lösung

\frac{d}{d x} (ln (sinh (5 x)))

Lösung

5 coth (5 x)

Schritte zur Lösung

\frac{d}{d x} (ln (sinh (5 x)))

Wende die Kettenregel an:

\frac{1}{sinh ( 5 x )} \frac{d}{d x} (sinh (5 x))

= \frac{1}{sinh ( 5 x )} \frac{d}{d x} (sinh (5 x))

\frac{d}{d x} (sinh (5 x)) = cosh (5 x) \cdot 5

= \frac{1}{sinh ( 5 x )} cosh (5 x) \cdot 5

Vereinfache

\frac{1}{sinh ( 5 x )} cosh (5 x) \cdot 5 : 5 coth (5 x)

= 5 coth (5 x)

Graph

Beliebte Beispiele

derivative y=(3x-2x^2)^3

d er i v a t i v e y = (3 x - 2 x^{2})^{3}

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(dy}{dx}=\frac{xsec(y/x)+y)/x

\frac{d y}{d x} = \frac{x sec ( \frac{y}{x} ) + y}{x}

integral of (x^2+3)^32x

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

(\partial)/(\partial x)(x^5y^5)

\frac{\partial}{\partial x} (x^{5} y^{5})