(\partial)/(\partial x)(sqrt(x^2+16))

Lösung

\frac{\partial}{\partial x} (x^{2} + 16)

\frac{x}{x ^{2} + 16}

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{2} + 16)

Wende die Kettenregel an:

\frac{1}{2 x ^{2} + 16} \frac{\partial}{\partial x} (x^{2} + 16)

= \frac{1}{2 x ^{2} + 16} \frac{\partial}{\partial x} (x^{2} + 16)

\frac{\partial}{\partial x} (x^{2} + 16) = 2 x

= \frac{1}{2 x ^{2} + 16} \cdot 2 x

Vereinfache

\frac{1}{2 x ^{2} + 16} \cdot 2 x : \frac{x}{x ^{2} + 16}

= \frac{x}{x ^{2} + 16}

θ \to 0 lim (\frac{sin ^{2} ( θ )}{θ})

\frac{d}{d x} ((5 x^{6} + 4 x^{3})^{4})

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t an g e n t f (x) = (9 x^{9} - 9) (8 - 8 x^{8}), at x = 0

\int - \frac{1}{sin ( x )} d x