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Beliebt Rechnen >

derivative of-3^{-2}(tan(7x)^5)

Lösung

\frac{d}{d x} (- 3^{- 2} (tan (7 x))^{5})

Lösung

- \frac{35}{9} tan^{4} (7 x) sec^{2} (7 x)

Schritte zur Lösung

\frac{d}{d x} (- 3^{- 2} (tan (7 x))^{5})

Entferne die Konstante:

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

= - 3^{- 2} \frac{d}{d x} ((tan (7 x))^{5})

Wende die Kettenregel an:

5 (tan (7 x))^{4} \frac{d}{d x} (tan (7 x))

= 5 (tan (7 x))^{4} \frac{d}{d x} (tan (7 x))

\frac{d}{d x} (tan (7 x)) = sec^{2} (7 x) \cdot 7

= - 3^{- 2} \cdot 5 (tan (7 x))^{4} sec^{2} (7 x) \cdot 7

Vereinfache

- 3^{- 2} \cdot 5 tan^{4} (7 x) sec^{2} (7 x) \cdot 7 : - \frac{35}{9} tan^{4} (7 x) sec^{2} (7 x)

= - \frac{35}{9} tan^{4} (7 x) sec^{2} (7 x)

Graph

Beliebte Beispiele

(2 cos (x))^{^{'}}

fläche y^2=x-2,y=x-4

a re a y^{2} = x - 2, y = x - 4

integral of (sec(2x)+tan(2x))

\int (sec (2 x) + tan (2 x)) d x

derivative f(x)=(2t+1)/(t+3)

d er i v a t i v e f (x) = \frac{2 t + 1}{t + 3}

fläche y=2x^2+3,(0,3)

a re a y = 2 x^{2} + 3, (0, 3)