derivative of x^5+5x^4-10x^2+6

Lösung

\frac{d}{d x} (x^{5} + 5 x^{4} - 10 x^{2} + 6)

5 x^{4} + 20 x^{3} - 20 x

Schritte zur Lösung

\frac{d}{d x} (x^{5} + 5 x^{4} - 10 x^{2} + 6)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x^{5}) + \frac{d}{d x} (5 x^{4}) - \frac{d}{d x} (10 x^{2}) + \frac{d}{d x} (6)

\frac{d}{d x} (x^{5}) = 5 x^{4}

\frac{d}{d x} (5 x^{4}) = 20 x^{3}

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

\frac{d}{d x} (6) = 0

= 5 x^{4} + 20 x^{3} - 20 x + 0

Vereinfache

= 5 x^{4} + 20 x^{3} - 20 x

im pl i c i t \frac{d y}{d x}, 2 x^{4} + 9 y = 2 x^{2} y + 36

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

in v erse l a pl a ce \frac{( s )}{s ^{2} + 5 s + 6}

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

\frac{d y}{d x} + 10 y = 8