(\partial)/(\partial x)((x^2+y^2+z^2)^{0.5})

Lösung

\frac{\partial}{\partial x} ((x^{2} + y^{2} + z^{2})^{0.5})

\frac{x}{( x ^{2} + y ^{2} + z ^{2} ) ^{\frac{1}{2}}}

Schritte zur Lösung

\frac{\partial}{\partial x} ((x^{2} + y^{2} + z^{2})^{0.5})

Behandle

y, z

als Konstanten

Wende die Kettenregel an:

\frac{0.5}{( x ^{2} + y ^{2} + z ^{2} ) ^{0.5}} \frac{\partial}{\partial x} (x^{2} + y^{2} + z^{2})

= \frac{0.5}{( x ^{2} + y ^{2} + z ^{2} ) ^{0.5}} \frac{\partial}{\partial x} (x^{2} + y^{2} + z^{2})

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

= \frac{0.5}{( x ^{2} + y ^{2} + z ^{2} ) ^{0.5}} \cdot 2 x

Vereinfache

\frac{0.5}{( x ^{2} + y ^{2} + z ^{2} ) ^{\frac{1}{2}}} \cdot 2 x : \frac{x}{( x ^{2} + y ^{2} + z ^{2} ) ^{\frac{1}{2}}}

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

\int \frac{4 - x}{x ^{4} - x ^{2}} d x

x \to 2 lim (2 x + c)

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

\frac{d y}{d x} = ∣ x - 2 ∣

t an g e n t f (x) = (x^{2} - 4)^{2}