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Beliebt Rechnen >

derivative f(x)=sqrt(x)sec(x)

Lösung

ableitung von

f (x) = x sec (x)

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (x sec (x))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = sec (x)

= \frac{d}{d x} (x) sec (x) + \frac{d}{d x} (sec (x)) x

\frac{d}{d x} (x) = \frac{1}{2 x}

\frac{d}{d x} (sec (x)) = sec (x) tan (x)

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

\frac{1}{2 x} sec (x) = \frac{sec ( x )}{2 x}

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

Graph

Beliebte Beispiele

derivative of x^2sqrt(x-4)

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

t a y l or cos (x)

limit as x approaches 0 of x^2-sin(1/x)

x \to 0 lim (x^{2} - sin (\frac{1}{x}))

derivative y=x^3(2x+3)^7

d er i v a t i v e y = x^{3} (2 x + 3)^{7}

fläche 3x, 3/x ,x=3

a re a 3 x, \frac{3}{x}, x = 3