What is the d/(d{y)}(({z}(y,x))({y}{x}^6-3{x}+8{x}^2{y}^2-{y}^2)) ?

The d/(d{y)}(({z}(y,x))({y}{x}^6-3{x}+8{x}^2{y}^2-{y}^2)) is {z}(y,x)({x}^6-0+16{y}{x}^2-2{y})

What is the first d/(d{y)}(({z}(y,x))({y}{x}^6-3{x}+8{x}^2{y}^2-{y}^2)) ?

The first d/(d{y)}(({z}(y,x))({y}{x}^6-3{x}+8{x}^2{y}^2-{y}^2)) is {z}(y,x)({x}^6-0+16{y}{x}^2-2{y})

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\frac{d}{d y} ((z (y, x)) (y x^{6} - 3 x + 8 x^{2} y^{2} - y^{2}))

z (y, x) (x^{6} - 0 + 16 y x^{2} - 2 y)

Solution steps

\frac{d}{d y} ((z (y, x)) (y x^{6} - 3 x + 8 x^{2} y^{2} - y^{2}))

Take the constant out:

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

= z (y, x) \frac{d}{d y} (y x^{6} - 3 x + 8 x^{2} y^{2} - y^{2})

Apply the Sum/Difference Rule:

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

= z (y, x) (\frac{d}{d y} (y x^{6}) - \frac{d}{d y} (3 x) + \frac{d}{d y} (8 x^{2} y^{2}) - \frac{d}{d y} (y^{2}))

\frac{d}{d y} (y x^{6}) = x^{6}

\frac{d}{d y} (3 x) = 0

\frac{d}{d y} (8 x^{2} y^{2}) = 16 y x^{2}

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

= z (y, x) (x^{6} - 0 + 16 y x^{2} - 2 y)

9 (- 6 + 2)

(e^{2 jπ} + e^{- 2 jπ})^{3}

(e^{16 i x} - 1) (e^{- 8 i x} + 3 e^{8 i x} + e^{16 i x} + 3)

- \frac{( 6 x - 5 ) ( x + 5 )}{( x - 6 ) ( x + 6 ) ( x - 5 )}

2 (5 - 3)

What is the d/(d{y)}(({z}(y,x))({y}{x}^6-3{x}+8{x}^2{y}^2-{y}^2)) ?
The d/(d{y)}(({z}(y,x))({y}{x}^6-3{x}+8{x}^2{y}^2-{y}^2)) is {z}(y,x)({x}^6-0+16{y}{x}^2-2{y})
What is the first d/(d{y)}(({z}(y,x))({y}{x}^6-3{x}+8{x}^2{y}^2-{y}^2)) ?
The first d/(d{y)}(({z}(y,x))({y}{x}^6-3{x}+8{x}^2{y}^2-{y}^2)) is {z}(y,x)({x}^6-0+16{y}{x}^2-2{y})