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

The d/(d{y)}(({z})({z}^3-{x}{y}+{y}{z}+{y}^3-2)) is {z}(3{y}^2+{z}-{x})

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

The first d/(d{y)}(({z})({z}^3-{x}{y}+{y}{z}+{y}^3-2)) is {z}(3{y}^2+{z}-{x})

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

z (3 y^{2} + z - x)

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d y} (z^{3}) = 0

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

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

\frac{d}{d y} (y^{3}) = 3 y^{2}

\frac{d}{d y} (2) = 0

= z (0 - x + z + 3 y^{2} - 0)

Simplify

= z (3 y^{2} + z - x)

\frac{1 + sin ( x ) ( 1 - sin ( x ) )}{cos ( x )}

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

24 e^{(- 20 t)} + 20 (\frac{6}{5} - \frac{6}{5} e^{(- 20 t)})

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

\frac{k ( 3 k + 7 )}{2}

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