derivative of sqrt(x)(x^2+1^{10})

Lösung

\frac{d}{d x} (x (x^{2} + 1)^{10})

\frac{( x ^{2} + 1 ) ^{10}}{2 x} + 20 x x (x^{2} + 1)^{9}

Schritte zur Lösung

\frac{d}{d x} (x (x^{2} + 1)^{10})

Wende die Produktregel an:

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

f = x, g = (x^{2} + 1)^{10}

= \frac{d}{d x} (x) (x^{2} + 1)^{10} + \frac{d}{d x} ((x^{2} + 1)^{10}) x

\frac{d}{d x} (x) = \frac{1}{2 x}

\frac{d}{d x} ((x^{2} + 1)^{10}) = 20 x (x^{2} + 1)^{9}

= \frac{1}{2 x} (x^{2} + 1)^{10} + 20 x (x^{2} + 1)^{9} x

\frac{1}{2 x} (x^{2} + 1)^{10} = \frac{( x ^{2} + 1 ) ^{10}}{2 x}

= \frac{( x ^{2} + 1 ) ^{10}}{2 x} + 20 x x (x^{2} + 1)^{9}

\int - \frac{1}{Ux} + \frac{1}{U ( x - U )} d x

\frac{\partial}{\partial y} (\frac{e ^{y}}{x + y ^{2}})

t an g e n t \frac{6}{3 x ^{2}} - x, at x = 1

\frac{d y}{d x} = 17

\frac{\partial}{\partial x} (y cos (π x))