(d^2)/(d{x)d{y}}(({f}(x,y))6({x}+{y})^2)

Lösung

\frac{d ^{2}}{d x d y} ((f (x, y)) 6 (x + y)^{2})

f (x, y) \cdot 6 \cdot 2 ((\frac{d}{d y} (x) + 1) (1 + 0) + 0 \cdot (x + y))

Schritte zur Lösung

\frac{d ^{2}}{d x d y} ((f (x, y)) \cdot 6 (x + y)^{2})

\frac{d}{d x} (f (x, y) \cdot 6 (x + y)^{2}) = f (x, y) \cdot 6 \cdot 2 (x + y) (1 + \frac{d}{d x} (y))

= \frac{d}{d y} (f (x, y) \cdot 6 \cdot 2 (x + y) (1 + \frac{d}{d x} (y)))

\frac{d}{d y} (f (x, y) \cdot 6 \cdot 2 (x + y) (1 + \frac{d}{d x} (y))) = f (x, y) \cdot 6 \cdot 2 ((\frac{d}{d y} (x) + 1) (1 + 0) + 0 \cdot (x + y))

= f (x, y) \cdot 6 \cdot 2 ((\frac{d}{d y} (x) + 1) (1 + 0) + 0 \cdot (x + y))

\frac{d ^{2}}{d x ^{2}} ((y) (2 x^{3} + y + y^{2}))

e x p an d (x 1 + x) (1 + 1 + x)

\frac{\partial}{\partial y} ((z) (3 x^{2} y + 4 x y^{2}))

s im pl i f y (- 2 b - 3 c)^{2}

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