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Popular >

d/(d{x)}(({z}(x,y))({x}{y}^5-{x}^2{y}))

Solution

\frac{d}{d x} ((z (x, y)) (x y^{5} - x^{2} y))

Solution

z (x, y) (y^{5} - 2 x y)

Solution steps

\frac{d}{d x} ((z (x, y)) (x y^{5} - x^{2} y))

Take the constant out:

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

= z (x, y) \frac{d}{d x} (x y^{5} - x^{2} y)

Apply the Sum/Difference Rule:

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

= z (x, y) (\frac{d}{d x} (x y^{5}) - \frac{d}{d x} (x^{2} y))

\frac{d}{d x} (x y^{5}) = y^{5}

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

= z (x, y) (y^{5} - 2 x y)

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Frequently Asked Questions (FAQ)

What is the d/(d{x)}(({z}(x,y))({x}{y}^5-{x}^2{y})) ?
The d/(d{x)}(({z}(x,y))({x}{y}^5-{x}^2{y})) is {z}(x,y)({y}^5-2{x}{y})
What is the first d/(d{x)}(({z}(x,y))({x}{y}^5-{x}^2{y})) ?
The first d/(d{x)}(({z}(x,y))({x}{y}^5-{x}^2{y})) is {z}(x,y)({y}^5-2{x}{y})