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Beliebt Rechnen >

derivative of 1/(cos(x)+1/(sin(x+1)))

Lösung

\frac{d}{d x} (\frac{1}{cos ( x )} + \frac{1}{sin ( x + 1 )})

Lösung

sec (x) tan (x) - cot (x + 1) csc (x + 1)

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{cos ( x )} + \frac{1}{sin ( x + 1 )})

Vereinfache

\frac{1}{cos ( x )} + \frac{1}{sin ( x + 1 )} : sec (x) + csc (x + 1)

= \frac{d}{d x} (sec (x) + csc (x + 1))

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (sec (x)) + \frac{d}{d x} (csc (x + 1))

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

\frac{d}{d x} (csc (x + 1)) = - cot (x + 1) csc (x + 1)

= sec (x) tan (x) - cot (x + 1) csc (x + 1)

Graph

Beliebte Beispiele

d/(dθ)((e^{iθ}+e^{-iθ})/2)

\frac{d}{d θ} (\frac{e ^{i θ} + e ^{- i θ}}{2})

derivative y=(t-sqrt(t))/(t^{1/3)}

d er i v a t i v e y = \frac{t - t}{t ^{\frac{1}{3}}}

integral of (4x+5)/(x^2+1)

\int \frac{4 x + 5}{x ^{2} + 1} d x

derivative of x^2*e^{4x}

\frac{d}{d x} (x^{2} \cdot e^{4 x})

integral of 3sqrt(x)-6x

\int 3 x - 6 x d x