derivative of ({Q}(x,y)(x^2+y(x,d)^2)dy(x,d))

Lösung

\frac{d}{d x} ((Q (x, y)) (x^{2} + y (x, d) (x, d)^{2}) d y (x, d))

d (\frac{d}{d x} (Q (x, y)) (x^{2} + y (x, d) (x, d)^{2}) y (x, d) + ((2 x + (\frac{d}{d x} (y (x, d)) (x, d)^{2} + 2 (x, d) (, d \cdot 1) y (x, d))) y (x, d) + \frac{d}{d x} (y (x, d)) (x^{2} + y (x, d) (x, d)^{2})) Q (x, y))

Schritte zur Lösung

\frac{d}{d x} ((Q (x, y)) (x^{2} + y (x, d) (x, d)^{2}) d y (x, d))

Behandle

d

als Konstante

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = Q (x, y), g = (x^{2} + y (x, d) (x, d)^{2}) y (x, d)

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

\frac{d}{d x} ((x^{2} + y (x, d) (x, d)^{2}) y (x, d)) = (2 x + (\frac{d}{d x} (y (x, d)) (x, d)^{2} + 2 (x, d) (, d \cdot 1) y (x, d))) y (x, d) + \frac{d}{d x} (y (x, d)) (x^{2} + y (x, d) (x, d)^{2})

= d (\frac{d}{d x} (Q (x, y)) (x^{2} + y (x, d) (x, d)^{2}) y (x, d) + ((2 x + (\frac{d}{d x} (y (x, d)) (x, d)^{2} + 2 (x, d) (, d \cdot 1) y (x, d))) y (x, d) + \frac{d}{d x} (y (x, d)) (x^{2} + y (x, d) (x, d)^{2})) Q (x, y))

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

e x p an d \frac{( 2 x - 1 ) ( 3 - x )}{( x - 1 ) ( x + 3 )}

e x p an d (0.2 s + 10) \frac{d}{d s} (0.2 s + 10)

e x p an d A (3, - 1, - 2) e B (1, 2, 4)

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