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Beliebt Rechnen >

derivative of tan^2(xcos(x))

Lösung

\frac{d}{d x} (tan^{2} (x) cos (x))

Lösung

sin (x) (1 + sec^{2} (x))

Schritte zur Lösung

\frac{d}{d x} (tan^{2} (x) cos (x))

Vereinfache

tan^{2} (x) cos (x) : sin (x) tan (x)

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

Wende die Produktregel an:

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

f = sin (x), g = tan (x)

= \frac{d}{d x} (sin (x)) tan (x) + \frac{d}{d x} (tan (x)) sin (x)

\frac{d}{d x} (sin (x)) = cos (x)

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

= cos (x) tan (x) + sec^{2} (x) sin (x)

Vereinfache

cos (x) tan (x) + sec^{2} (x) sin (x) : sin (x) (1 + sec^{2} (x))

= sin (x) (1 + sec^{2} (x))

Graph

Beliebte Beispiele

sum from n=0 to infinity of 6(3/4)^n

n = 0 \sum \infty 6 (\frac{3}{4})^{n}

integral of (ln(11x))^2

\int (ln (11 x))^{2} d x

derivative sqrt(3x+7)

d er i v a t i v e 3 x + 7

derivative-2.25cos(1.5x)

d er i v a t i v e - 2.25 cos (1.5 x)

integral from 0 to 33 of (x-1)^{-1/5}

\int_{0}^{33} (x - 1)^{- \frac{1}{5}} d x