derivative of 4x^5-3x^m+2x^n+5x^2-x-6

Lösung

\frac{d}{d x} (4 x^{5} - 3 x^{m} + 2 x^{n} + 5 x^{2} - x - 6)

20 x^{4} + 10 x + 2 n x^{n - 1} - 3 m x^{m - 1} - 1

Schritte zur Lösung

\frac{d}{d x} (4 x^{5} - 3 x^{m} + 2 x^{n} + 5 x^{2} - x - 6)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (4 x^{5}) - \frac{d}{d x} (3 x^{m}) + \frac{d}{d x} (2 x^{n}) + \frac{d}{d x} (5 x^{2}) - \frac{d x}{d x} - \frac{d}{d x} (6)

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

\frac{d}{d x} (3 x^{m}) = 3 m x^{m - 1}

\frac{d}{d x} (2 x^{n}) = 2 n x^{n - 1}

\frac{d}{d x} (5 x^{2}) = 10 x

\frac{d x}{d x} = 1

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

= 20 x^{4} - 3 m x^{m - 1} + 2 n x^{n - 1} + 10 x - 1 - 0

Vereinfache

= 20 x^{4} + 10 x + 2 n x^{n - 1} - 3 m x^{m - 1} - 1

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

\int 3 4 x^{3} - 8 x^{5} + 6 e^{x} - 2 d x

x^{^{'}} = - x + sin (t)

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

x \to 8 lim (\frac{1}{( x - 8 ) ^{2}})