derivative y=(2tan^2(2x)-1)^{1/2}

Lösung

ableitung von

y = (2 tan^{2} (2 x) - 1)^{\frac{1}{2}}

\frac{4 sec ^{2} ( 2 x ) tan ( 2 x )}{( 2 tan ^{2} ( 2 x ) - 1 ) ^{\frac{1}{2}}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (2 tan^{2} (2 x) - 1) = 8 sec^{2} (2 x) tan (2 x)

= \frac{1}{2 ( 2 tan ^{2} ( 2 x ) - 1 ) ^{\frac{1}{2}}} \cdot 8 sec^{2} (2 x) tan (2 x)

Vereinfache

\frac{1}{2 ( 2 tan ^{2} ( 2 x ) - 1 ) ^{\frac{1}{2}}} \cdot 8 sec^{2} (2 x) tan (2 x) : \frac{4 sec ^{2} ( 2 x ) tan ( 2 x )}{( 2 tan ^{2} ( 2 x ) - 1 ) ^{\frac{1}{2}}}

= \frac{4 sec ^{2} ( 2 x ) tan ( 2 x )}{( 2 tan ^{2} ( 2 x ) - 1 ) ^{\frac{1}{2}}}

\frac{\partial}{\partial x} (x (1 - x - 2 y))

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d er i v a t i v e π^{2}

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