What is the d/(dy)((x)(x^4+y^2)) ?

The d/(dy)((x)(x^4+y^2)) is 2xy

What is the first d/(dy)((x)(x^4+y^2)) ?

The first d/(dy)((x)(x^4+y^2)) is 2xy

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\frac{d}{d y} ((x) (x^{4} + y^{2}))

2 x y

Solution steps

\frac{d}{d y} ((x) (x^{4} + y^{2}))

Treat

x

as a constant

Take the constant out:

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

= x \frac{d}{d y} (x^{4} + y^{2})

Apply the Sum/Difference Rule:

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

= x (\frac{d}{d y} (x^{4}) + \frac{d}{d y} (y^{2}))

\frac{d}{d y} (x^{4}) = 0

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

= x (0 + 2 y)

Simplify

= 2 x y

\frac{2}{9 ( 1 - 2 x )}

\frac{30 ( 3600 + x ^{2} )}{x ^{2}}

\frac{5}{( 2 x + 1 ) ^{2}}

\frac{6 x + 3}{( x - 4 ) ^{2} ( x - 2 )}

\frac{9 x ^{2} - 18 x - 3}{( x - 2 ) ^{2}}