derivative of ((x+5^5-1)^4)

Lösung

\frac{d}{d x} (((x + 5)^{5} - 1)^{4})

4 (x^{5} + 25 x^{4} + 250 x^{3} + 1250 x^{2} + 3125 x + 3124)^{3} (5 x^{4} + 100 x^{3} + 750 x^{2} + 2500 x + 3125)

Schritte zur Lösung

\frac{d}{d x} (((x + 5)^{5} - 1)^{4})

Vereinfache

((x + 5)^{5} - 1)^{4} : (x^{5} + 25 x^{4} + 250 x^{3} + 1250 x^{2} + 3125 x + 3124)^{4}

= \frac{d}{d x} ((x^{5} + 25 x^{4} + 250 x^{3} + 1250 x^{2} + 3125 x + 3124)^{4})

Wende die Kettenregel an:

4 (x^{5} + 25 x^{4} + 250 x^{3} + 1250 x^{2} + 3125 x + 3124)^{3} \frac{d}{d x} (x^{5} + 25 x^{4} + 250 x^{3} + 1250 x^{2} + 3125 x + 3124)

= 4 (x^{5} + 25 x^{4} + 250 x^{3} + 1250 x^{2} + 3125 x + 3124)^{3} \frac{d}{d x} (x^{5} + 25 x^{4} + 250 x^{3} + 1250 x^{2} + 3125 x + 3124)

\frac{d}{d x} (x^{5} + 25 x^{4} + 250 x^{3} + 1250 x^{2} + 3125 x + 3124) = 5 x^{4} + 100 x^{3} + 750 x^{2} + 2500 x + 3125

= 4 (x^{5} + 25 x^{4} + 250 x^{3} + 1250 x^{2} + 3125 x + 3124)^{3} (5 x^{4} + 100 x^{3} + 750 x^{2} + 2500 x + 3125)

\frac{\partial}{\partial x} (\frac{1}{1 - e ^{- x}})

x \to 0 lim (x cot (\frac{10}{3} x))

d er i v a t i v e y = x^{2} 8 x - 9

y^{^{''}} + 4 y = sec^{3} (2 x)

t an g e n t y = arctan (- x), at x = 3