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Beliebt Rechnen >

derivative of xsec^2(pix)

Lösung

\frac{d}{d x} (x sec^{2} (π x))

Lösung

sec^{2} (π x) + 2 π x sec^{2} (π x) tan (π x)

Schritte zur Lösung

\frac{d}{d x} (x sec^{2} (π x))

Wende die Produktregel an:

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

f = x, g = sec^{2} (π x)

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

\frac{d x}{d x} = 1

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

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

Vereinfache

= sec^{2} (π x) + 2 π x sec^{2} (π x) tan (π x)

Graph

Beliebte Beispiele

limit as x approaches-0 of 2xe^{2x}+kx

x \to - 0 lim (2 x e^{2 x} + k x)

integral of 1+2/t

\int 1 + \frac{2}{t} d t

integral of (cos(x)+1/3 x)

\int (cos (x) + \frac{1}{3} x) d x

integral of e^{x-1}+x^{-2}

\int e^{x - 1} + x^{- 2} d x

integral of-x^2+3x

\int - x^{2} + 3 x d x