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Beliebt Rechnen >

derivative of x^2arctan(5x+ln(1+4x^2))

Lösung

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

Lösung

2 x arctan (5 x) + \frac{5 x ^{2}}{25 x ^{2} + 1} + \frac{8 x}{1 + 4 x ^{2}}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (x^{2} arctan (5 x)) = 2 x arctan (5 x) + \frac{5 x ^{2}}{25 x ^{2} + 1}

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

= 2 x arctan (5 x) + \frac{5 x ^{2}}{25 x ^{2} + 1} + \frac{8 x}{1 + 4 x ^{2}}

Graph

Beliebte Beispiele

derivative of 9sin(4x)

\frac{d}{d x} (9 sin (4 x))

derivative (36)/((1+3x)^3)

d er i v a t i v e \frac{36}{( 1 + 3 x ) ^{3}}

integral of (26)/((x^2-1)^2)

\int \frac{26}{( x ^{2} - 1 ) ^{2}} d x

inverselaplace (0.07s)/(7s^2+19980)

in v erse l a pl a ce \frac{0.07 s}{7 s ^{2} + 19980}

fläche e^{-7x},x>= 0

a re a e^{- 7 x}, x \geq 0