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Beliebt Rechnen >

derivative of 1/2 (tan(x-x))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Verwende die Pythagoreische Identität:

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

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

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

Graph

Beliebte Beispiele

sum from n=0 to infinity of n^3x^n

n = 0 \sum \infty n^{3} x^{n}

derivative of 9xarcsin(x)

\frac{d}{d x} (9 x arcsin (x))

derivative of sqrt(6x-5)

\frac{d}{d x} (6 x - 5)

integral of (x^3-2x+3)/(x-1)

\int \frac{x ^{3} - 2 x + 3}{x - 1} d x

inverselaplace 1/((s+4)^2)

in v erse l a pl a ce \frac{1}{( s + 4 ) ^{2}}