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Popular >

d/(dy)((x)(x^4y^3+8x^2y))

Solution

\frac{d}{d y} ((x) (x^{4} y^{3} + 8 x^{2} y))

Solution

x (3 x^{4} y^{2} + 8 x^{2})

Solution steps

\frac{d}{d y} ((x) (x^{4} y^{3} + 8 x^{2} y))

Treat

x

as a constant

Take the constant out:

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

= x \frac{d}{d y} (x^{4} y^{3} + 8 x^{2} y)

Apply the Sum/Difference Rule:

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

= x (\frac{d}{d y} (x^{4} y^{3}) + \frac{d}{d y} (8 x^{2} y))

\frac{d}{d y} (x^{4} y^{3}) = 3 x^{4} y^{2}

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

= x (3 x^{4} y^{2} + 8 x^{2})

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Frequently Asked Questions (FAQ)

What is the d/(dy)((x)(x^4y^3+8x^2y)) ?
The d/(dy)((x)(x^4y^3+8x^2y)) is x(3x^4y^2+8x^2)
What is the first d/(dy)((x)(x^4y^3+8x^2y)) ?
The first d/(dy)((x)(x^4y^3+8x^2y)) is x(3x^4y^2+8x^2)