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Popular >

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

Solution

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

Solution

z (z^{3} + y)

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (x z^{3}) = z^{3}

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

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

Simplify

= z (z^{3} + y)

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Frequently Asked Questions (FAQ)

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