d/(dy)((x)((5x+2y)^8))

Lösung

\frac{d}{d y} ((x) ((5 x + 2 y)^{8}))

16 x (5 x + 2 y)^{7}

Schritte zur Lösung

\frac{d}{d y} ((x) ((5 x + 2 y)^{8}))

Behandle

x

als Konstante

Entferne die Konstante:

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

= x \frac{d}{d y} ((5 x + 2 y)^{8})

Wende die Kettenregel an:

8 (5 x + 2 y)^{7} \frac{d}{d y} (5 x + 2 y)

= 8 (5 x + 2 y)^{7} \frac{d}{d y} (5 x + 2 y)

\frac{d}{d y} (5 x + 2 y) = 2

= x \cdot 8 (5 x + 2 y)^{7} \cdot 2

Vereinfache

= 16 x (5 x + 2 y)^{7}

e x p an d (2 i) (3 i^{2}) (5)

e x p an d \frac{x ^{4} - x ^{3} - 13 x ^{2} + 2 x + 6}{( x + 3 ) ( x + 4 )}

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e x p an d (\frac{1}{x ^{2}} + y^{2}) (x d y - y d x)

e x p an d - \frac{1}{( z - 1 ) ( z - 2 )}