derivative of sqrt(5+tan^2(x))

Lösung

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

\frac{sec ^{2} ( x ) tan ( x )}{5 + tan ^{2} ( x )}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (5 + tan^{2} (x)) = 2 sec^{2} (x) tan (x)

= \frac{1}{2 5 + tan ^{2} ( x )} \cdot 2 sec^{2} (x) tan (x)

Vereinfache

\frac{1}{2 5 + tan ^{2} ( x )} \cdot 2 sec^{2} (x) tan (x) : \frac{sec ^{2} ( x ) tan ( x )}{5 + tan ^{2} ( x )}

= \frac{sec ^{2} ( x ) tan ( x )}{5 + tan ^{2} ( x )}

\frac{\partial}{\partial y} (y^{6} sin (4 x))

\int_{0}^{1} 1 + x d x

\int_{0}^{1} π (1 - x^{2})^{2} d x

(3 + 4 x) + (5 y - 1) \frac{d y}{d x} = 0

t an g e n t f (x) = x^{2} + 5 x - 2, at x = 4