d/(dy)((x)(1+sin((pix)/4)))

Lösung

\frac{d}{d y} ((y) (1 + sin (\frac{π y}{4})))

1 + sin (\frac{π y}{4}) + \frac{π y cos ( \frac{π y}{4} )}{4}

Schritte zur Lösung

\frac{d}{d y} ((y) (1 + sin (\frac{π y}{4})))

Wende die Produktregel an:

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

f = y, g = 1 + sin (\frac{π y}{4})

= \frac{d y}{d y} (1 + sin (\frac{π y}{4})) + \frac{d}{d y} (1 + sin (\frac{π y}{4})) y

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

\frac{d}{d y} (1 + sin (\frac{π y}{4})) = \frac{π}{4} cos (\frac{π y}{4})

= 1 \cdot (1 + sin (\frac{π y}{4})) + \frac{π}{4} cos (\frac{π y}{4}) y

Vereinfache

1 \cdot (1 + sin (\frac{π y}{4})) + \frac{π}{4} cos (\frac{π y}{4}) y : 1 + sin (\frac{π y}{4}) + \frac{π y cos ( \frac{π y}{4} )}{4}

= 1 + sin (\frac{π y}{4}) + \frac{π y cos ( \frac{π y}{4} )}{4}

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

e x p an d \frac{( 2 x + 1 ) ^{4}}{x ^{2} + x + 2}

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

e x p an d \frac{20 x ^{3}}{4 x}

e x p an d - 1 (y - x = 10)