What is the d/(dy)((x)(xy^2+{g}(y))) ?

The d/(dy)((x)(xy^2+{g}(y))) is x(2xy+d/(dy)({g}(y)))

What is the first d/(dy)((x)(xy^2+{g}(y))) ?

The first d/(dy)((x)(xy^2+{g}(y))) is x(2xy+d/(dy)({g}(y)))

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

x (2 x y + \frac{d}{d y} (g (y)))

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

= x (2 x y + \frac{d}{d y} (g (y)))

3 x + x - 9

- (x - 5) (x + 3)

\frac{( x - 2 ) ( x + 4 )}{( x - 1 ) ( x - 4 )}

(2 p x y) d x + (x^{2} + p y^{2}) d y

b (a (a + b))

What is the d/(dy)((x)(xy^2+{g}(y))) ?
The d/(dy)((x)(xy^2+{g}(y))) is x(2xy+d/(dy)({g}(y)))
What is the first d/(dy)((x)(xy^2+{g}(y))) ?
The first d/(dy)((x)(xy^2+{g}(y))) is x(2xy+d/(dy)({g}(y)))