(\partial)/(\partial x)(5x^3+4x+(7-x)^2)

Lösung

\frac{\partial}{\partial x} (5 x^{3} + 4 x + (7 - x)^{2})

15 x^{2} + 2 x - 10

Schritte zur Lösung

\frac{\partial}{\partial x} (5 x^{3} + 4 x + (7 - x)^{2})

Vereinfache

5 x^{3} + 4 x + (7 - x)^{2} : 5 x^{3} + x^{2} - 10 x + 49

= \frac{\partial}{\partial x} (5 x^{3} + x^{2} - 10 x + 49)

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (5 x^{3}) + \frac{\partial}{\partial x} (x^{2}) - \frac{\partial}{\partial x} (10 x) + \frac{\partial}{\partial x} (49)

\frac{\partial}{\partial x} (5 x^{3}) = 15 x^{2}

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

\frac{\partial}{\partial x} (10 x) = 10

\frac{\partial}{\partial x} (49) = 0

= 15 x^{2} + 2 x - 10 + 0

Vereinfache

= 15 x^{2} + 2 x - 10

\int \frac{4 x ^{3}}{2 x + 3} d x

d er i v a t i v e π r^{2} h

\int \frac{1}{x ^{2} x ^{2} - 9} d x

\frac{\partial}{\partial x} (4 x - 2 y + 3)

n = 1 \sum \infty \frac{x ^{n}}{n + 2}