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Beliebt Rechnen >

derivative of xtanh(x)

Lösung

\frac{d}{d x} (x tanh (x))

Lösung

tanh (x) + x sech^{2} (x)

Schritte zur Lösung

\frac{d}{d x} (x tanh (x))

Wende die Produktregel an:

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

f = x, g = tanh (x)

= \frac{d x}{d x} tanh (x) + \frac{d}{d x} (tanh (x)) x

\frac{d x}{d x} = 1

\frac{d}{d x} (tanh (x)) = sech^{2} (x)

= 1 \cdot tanh (x) + sech^{2} (x) x

Vereinfache

= tanh (x) + x sech^{2} (x)

Graph

Beliebte Beispiele

integral from 0 to 4 of (4x-x^2)^2

\int_{0}^{4} (4 x - x^{2})^{2} d x

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

\frac{d}{d x} ((x - 2)^{2} - 3 x)

derivative of xlog_{e}(2x)

\frac{d}{d x} (x lo g_{e} (2 x))

y^{''} (t)

tangent f(x)=3-2xe^x,\at x=0

t an g e n t f (x) = 3 - 2 x e^{x}, at x = 0