derivative of (y^2(5sin(x)+5cos(x)))

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

\frac{d}{d x} (5 sin (x) + 5 cos (x)) = 5 cos (x) - 5 sin (x)

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

s im pl i f y (s^{2} + 4) \cdot (s^{2} + \frac{4}{3})

s im pl i f y (- 3 x + 2 + 1)^{2}

e x p an d \frac{( - y + 4 ) ^{3}}{24}

e x p an d (\frac{5}{3 x} + \frac{5}{x} = 1) 3 x

s im pl i f y (- \frac{5}{2} - x) (- 3 - x) - 3