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Beliebt Rechnen >

derivative of cosh(xsinh(x))

Lösung

\frac{d}{d x} (cosh (x) sinh (x))

Lösung

sinh^{2} (x) + cosh^{2} (x)

Schritte zur Lösung

\frac{d}{d x} (cosh (x) sinh (x))

Wende die Produktregel an:

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

f = cosh (x), g = sinh (x)

= \frac{d}{d x} (cosh (x)) sinh (x) + \frac{d}{d x} (sinh (x)) cosh (x)

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

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

= sinh (x) sinh (x) + cosh (x) cosh (x)

Vereinfache

sinh (x) sinh (x) + cosh (x) cosh (x) : sinh^{2} (x) + cosh^{2} (x)

= sinh^{2} (x) + cosh^{2} (x)

Graph

Beliebte Beispiele

derivative of (((-2x-1)/((-4x+2)))^5)

\frac{d}{d x} ((\frac{( - 2 x - 1 )}{( - 4 x + 2 )})^{5})

derivative 1/(x^{2/3)}

d er i v a t i v e \frac{1}{x ^{\frac{2}{3}}}

inverselaplace 6/(s(s+2))

in v erse l a pl a ce \frac{6}{s ( s + 2 )}

derivative 3x^2-8x-sqrt(x)

d er i v a t i v e 3 x^{2} - 8 x - x

integral of x/((x^2+z^2)^{3/2)}

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