derivative of x^2tanh(1/x)

Lösung

\frac{d}{d x} (x^{2} tanh (\frac{1}{x}))

2 x tanh (\frac{1}{x}) - sech^{2} (\frac{1}{x})

Schritte zur Lösung

\frac{d}{d x} (x^{2} tanh (\frac{1}{x}))

Wende die Produktregel an:

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

f = x^{2}, g = tanh (\frac{1}{x})

= \frac{d}{d x} (x^{2}) tanh (\frac{1}{x}) + \frac{d}{d x} (tanh (\frac{1}{x})) x^{2}

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

\frac{d}{d x} (tanh (\frac{1}{x})) = - \frac{sech ^{2} ( \frac{1}{x} )}{x ^{2}}

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

Vereinfache

2 x tanh (\frac{1}{x}) + (- \frac{sech ^{2} ( \frac{1}{x} )}{x ^{2}}) x^{2} : 2 x tanh (\frac{1}{x}) - sech^{2} (\frac{1}{x})

= 2 x tanh (\frac{1}{x}) - sech^{2} (\frac{1}{x})

d er i v a t i v e \frac{( 10 y ^{3} - 9 y ^{2} + 6 y - 10 )}{( 2 y + 3 )}

5 x^{^{''}} + 20 x^{^{'}} + 20 x = 28

\int sin^{3} (x) \cdot cos^{2} (x) d x

\int arcsin (b x) d x

\int \frac{3 x}{1 - 9 x ^{4}} d x