derivative y=arctan(sqrt(7x^2-1))

Lösung

ableitung von

y = arctan (7 x^{2} - 1)

\frac{1}{x 7 x ^{2} - 1}

Schritte zur Lösung

\frac{d}{d x} (arctan (7 x^{2} - 1))

Wende die Kettenregel an:

\frac{1}{( 7 x ^{2} - 1 ) ^{2} + 1} \frac{d}{d x} (7 x^{2} - 1)

= \frac{1}{( 7 x ^{2} - 1 ) ^{2} + 1} \frac{d}{d x} (7 x^{2} - 1)

\frac{d}{d x} (7 x^{2} - 1) = \frac{7 x}{7 x ^{2} - 1}

= \frac{1}{( 7 x ^{2} - 1 ) ^{2} + 1} \cdot \frac{7 x}{7 x ^{2} - 1}

Vereinfache

\frac{1}{( 7 x ^{2} - 1 ) ^{2} + 1} \cdot \frac{7 x}{7 x ^{2} - 1} : \frac{1}{x 7 x ^{2} - 1}

= \frac{1}{x 7 x ^{2} - 1}

\int x (cos^{2} (x)) d x

(x^{2} + 1) y^{^{'}} + 8 x (y - 1) = 0, y (0) = 3

\frac{\partial}{\partial x} (4 x^{2} - 4 x y + x yz)

\int (t^{2} - 1) (4 + 3 t) d t

t an g e n t f (x) = x^{4}, at x = 1