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Beliebt Rechnen >

derivative sin(x)tan(x)

Lösung

ableitung von

sin (x) tan (x)

Lösung

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

Schritte zur Lösung

\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

integral from 1 to 16 of 1/(2x)

\int_{1}^{16} \frac{1}{2 x} d x

integral of (-x+8)/(-x^2-x+8)

\int \frac{- x + 8}{- x ^{2} - x + 8} d x

limit as x approaches 1 of (1+x)/(1-x)

x \to 1 lim (\frac{1 + x}{1 - x})

taylor 1/(1+1x)

t a y l or \frac{1}{1 + 1 x}

y^{^{'}} + t y = t