derivative f(x)=sin(x^2)+(1-x)/(1+x)

Lösung

ableitung von

f (x) = sin (x^{2}) + \frac{1 - x}{1 + x}

cos (x^{2}) \cdot 2 x - \frac{2}{( 1 + x ) ^{2}}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (sin (x^{2})) = cos (x^{2}) \cdot 2 x

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

= cos (x^{2}) \cdot 2 x - \frac{2}{( 1 + x ) ^{2}}

\frac{d y}{d t} = 0.28 - \frac{( 7 y )}{1000}

\frac{d}{d x} (\frac{x ^{3}}{x ^{4} + 1})

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

\frac{d y}{d x} = \frac{4}{x ^{2} - 1}

x \to 1 + lim (\frac{1 + x}{1 - x})