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Beliebt Rechnen >

derivative of arcsinh(tan(x))

Lösung

\frac{d}{d x} (arcsinh (tan (x)))

Lösung

sec^{2} (x)

Schritte zur Lösung

\frac{d}{d x} (arcsinh (tan (x)))

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= sec^{2} (x)

Graph

Beliebte Beispiele

derivative of (1-2x/(4+x))

\frac{d}{d x} (\frac{1 - 2 x}{4 + x})

sum from n=0 to infinity of 4(2/3)^{2n}

n = 0 \sum \infty 4 (\frac{2}{3})^{2 n}

integral of x^{-7/4}

\int x^{- \frac{7}{4}} d x

derivative f(x)= x/(2(x^2+7)^{3/4)}

d er i v a t i v e f (x) = \frac{x}{2 ( x ^{2} + 7 ) ^{\frac{3}{4}}}

derivative of sin(5x+2)

\frac{d}{d x} (sin (5 x + 2))