derivative of sqrt(x^5+4x^2-1)

Lösung

\frac{d}{d x} (x^{5} + 4 x^{2} - 1)

\frac{5 x ^{4} + 8 x}{2 x ^{5} + 4 x ^{2} - 1}

Schritte zur Lösung

\frac{d}{d x} (x^{5} + 4 x^{2} - 1)

Wende die Kettenregel an:

\frac{1}{2 x ^{5} + 4 x ^{2} - 1} \frac{d}{d x} (x^{5} + 4 x^{2} - 1)

= \frac{1}{2 x ^{5} + 4 x ^{2} - 1} \frac{d}{d x} (x^{5} + 4 x^{2} - 1)

\frac{d}{d x} (x^{5} + 4 x^{2} - 1) = 5 x^{4} + 8 x

= \frac{1}{2 x ^{5} + 4 x ^{2} - 1} (5 x^{4} + 8 x)

Vereinfache

\frac{1}{2 x ^{5} + 4 x ^{2} - 1} (5 x^{4} + 8 x) : \frac{5 x ^{4} + 8 x}{2 x ^{5} + 4 x ^{2} - 1}

= \frac{5 x ^{4} + 8 x}{2 x ^{5} + 4 x ^{2} - 1}

d er i v a t i v e - 6 x

\frac{d}{d y} (y^{2} e^{x y})

\frac{d}{d x} (x csc (x) - cot (x))

n = 0 \sum \infty \frac{6}{2 ^{n}}

d er i v a t i v e f (x) = \frac{- 6}{x}