derivative of sqrt((3x+1/(5x^2+1)))

Lösung

\frac{d}{d x} (\frac{3 x + 1}{5 x ^{2} + 1})

\frac{- 15 x ^{2} - 10 x + 3}{2 3 x + 1 ( 5 x ^{2} + 1 ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x + 1}{5 x ^{2} + 1})

Wende die Kettenregel an:

\frac{1}{2 \frac{3 x + 1}{5 x ^{2} + 1}} \frac{d}{d x} (\frac{3 x + 1}{5 x ^{2} + 1})

= \frac{1}{2 \frac{3 x + 1}{5 x ^{2} + 1}} \frac{d}{d x} (\frac{3 x + 1}{5 x ^{2} + 1})

\frac{d}{d x} (\frac{3 x + 1}{5 x ^{2} + 1}) = \frac{- 15 x ^{2} - 10 x + 3}{( 5 x ^{2} + 1 ) ^{2}}

= \frac{1}{2 \frac{3 x + 1}{5 x ^{2} + 1}} \cdot \frac{- 15 x ^{2} - 10 x + 3}{( 5 x ^{2} + 1 ) ^{2}}

Vereinfache

\frac{1}{2 \frac{3 x + 1}{5 x ^{2} + 1}} \cdot \frac{- 15 x ^{2} - 10 x + 3}{( 5 x ^{2} + 1 ) ^{2}} : \frac{- 15 x ^{2} - 10 x + 3}{2 3 x + 1 ( 5 x ^{2} + 1 ) ^{\frac{3}{2}}}

= \frac{- 15 x ^{2} - 10 x + 3}{2 3 x + 1 ( 5 x ^{2} + 1 ) ^{\frac{3}{2}}}

d er i v a t i v e f (x) = \frac{sin ( x )}{x ^{3}}

x y^{^{'}} + y = 6 x^{2}, y (1) = 2

n \to \infty lim (n^{10})

d er i v a t i v e f (x) = 2 x - x ln ∣ x ∣

n = 0 \sum \infty \frac{1 ^{n}}{2 n + 1}