d/(dy)((x)(x^2+sin(5x)))

Lösung

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

3 y^{2} + 5 y cos (5 y) + sin (5 y)

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = y^{2} + sin (5 y)

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

\frac{d y}{d y} = 1

\frac{d}{d y} (y^{2} + sin (5 y)) = 2 y + cos (5 y) \cdot 5

= 1 \cdot (y^{2} + sin (5 y)) + (2 y + cos (5 y) \cdot 5) y

Vereinfache

1 \cdot (y^{2} + sin (5 y)) + (2 y + cos (5 y) \cdot 5) y : 3 y^{2} + 5 y cos (5 y) + sin (5 y)

= 3 y^{2} + 5 y cos (5 y) + sin (5 y)

e x p an d e l i p se (16 x^{2} - 4 x y + 16 y^{2} - 112 x - 136 y = 704)

e x p an d \frac{1}{5} e^{x} (e^{x} - 1)

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

e x p an d \frac{a + b}{2 ( a - b )}

e x p an d \frac{- x ^{2} + 2 x - 5}{( x - 2 ) ^{2} ( x + 3 ) ^{2}}