(\partial)/(\partial x)(sqrt(t^4+x^3))

Lösung

\frac{\partial}{\partial x} (t^{4} + x^{3})

\frac{3 x ^{2}}{2 t ^{4} + x ^{3}}

Schritte zur Lösung

\frac{\partial}{\partial x} (t^{4} + x^{3})

Behandle

t

als Konstante

Wende die Kettenregel an:

\frac{1}{2 t ^{4} + x ^{3}} \frac{\partial}{\partial x} (t^{4} + x^{3})

= \frac{1}{2 t ^{4} + x ^{3}} \frac{\partial}{\partial x} (t^{4} + x^{3})

\frac{\partial}{\partial x} (t^{4} + x^{3}) = 3 x^{2}

= \frac{1}{2 t ^{4} + x ^{3}} \cdot 3 x^{2}

Vereinfache

\frac{1}{2 t ^{4} + x ^{3}} \cdot 3 x^{2} : \frac{3 x ^{2}}{2 t ^{4} + x ^{3}}

= \frac{3 x ^{2}}{2 t ^{4} + x ^{3}}

\int 4 cos (x) d x

\int \frac{1}{22 - x ^{2}} d x

n = 0 \sum \infty 6 (\frac{1}{7})^{n}

x \to 2 - lim (\frac{x + 2}{x - 4})

n = - \infty \sum \infty 7^{2}