What is the d/(d{y)}(({f}(y,x))({x}^2{y}+{x}+{x}{y}^2+{y})) ?

The d/(d{y)}(({f}(y,x))({x}^2{y}+{x}+{x}{y}^2+{y})) is {f}(y,x)({x}^2+d/(d{y)}({x})+2{y}{x}+1)

What is the first d/(d{y)}(({f}(y,x))({x}^2{y}+{x}+{x}{y}^2+{y})) ?

The first d/(d{y)}(({f}(y,x))({x}^2{y}+{x}+{x}{y}^2+{y})) is {f}(y,x)({x}^2+d/(d{y)}({x})+2{y}{x}+1)

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

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

(x - 1) (x + 5) (x - 5)

\frac{( x + 3 ) ( x ^{2} - x + 2 )}{( x - 2 ) ( x ^{2} + 7 )}

(2 y sin (x) + x^{2})^{5}

- 1 + 2 (x - \frac{3 π}{4})

What is the d/(d{y)}(({f}(y,x))({x}^2{y}+{x}+{x}{y}^2+{y})) ?
The d/(d{y)}(({f}(y,x))({x}^2{y}+{x}+{x}{y}^2+{y})) is {f}(y,x)({x}^2+d/(d{y)}({x})+2{y}{x}+1)
What is the first d/(d{y)}(({f}(y,x))({x}^2{y}+{x}+{x}{y}^2+{y})) ?
The first d/(d{y)}(({f}(y,x))({x}^2{y}+{x}+{x}{y}^2+{y})) is {f}(y,x)({x}^2+d/(d{y)}({x})+2{y}{x}+1)