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Popular >

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

Solution

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

Solution

z (y, x) (5 y^{4} x - x^{2})

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d y} (x y^{5}) = 5 y^{4} x

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

= z (y, x) (5 y^{4} x - x^{2})

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Frequently Asked Questions (FAQ)

What is the d/(d{y)}(({z}(y,x))({x}{y}^5-{x}^2{y})) ?
The d/(d{y)}(({z}(y,x))({x}{y}^5-{x}^2{y})) is {z}(y,x)(5{y}^4{x}-{x}^2)
What is the first d/(d{y)}(({z}(y,x))({x}{y}^5-{x}^2{y})) ?
The first d/(d{y)}(({z}(y,x))({x}{y}^5-{x}^2{y})) is {z}(y,x)(5{y}^4{x}-{x}^2)