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Popular >

d/(dy)((y^3-8)/(y^3+8))

Solution

\frac{d}{d y} (\frac{y ^{3} - 8}{y ^{3} + 8})

Solution

\frac{48 y ^{2}}{( y ^{3} + 8 ) ^{2}}

Solution steps

\frac{d}{d y} (\frac{y ^{3} - 8}{y ^{3} + 8})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d y} (y^{3} - 8) = 3 y^{2}

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

= \frac{3 y ^{2} ( y ^{3} + 8 ) - 3 y ^{2} ( y ^{3} - 8 )}{( y ^{3} + 8 ) ^{2}}

Expand

3 y^{2} (y^{3} + 8) - 3 y^{2} (y^{3} - 8) : 48 y^{2}

= \frac{48 y ^{2}}{( y ^{3} + 8 ) ^{2}}

Graph

Popular Examples

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\int e^{x} (x^{2} + 2 x) d x

(\partial)/(\partial x)(xc^2(1/(sqrt(1-\frac{v^2){c^2)}}-1))

\frac{\partial}{\partial x} x c^{2} \frac{1}{1 - \frac{v ^{2}}{c ^{2}}} - 1

integral from 0 to 1 of t/((2-t)^2)

\int_{0}^{1} \frac{t}{( 2 - t ) ^{2}} d t

integral of 1/(xsqrt(144x^2-144))

\int \frac{1}{x 144 x ^{2} - 144} d x

tangent of f(x)= 2/(x-4),\at x=6 tangent of

f (x) = \frac{2}{x - 4}, at x = 6

Frequently Asked Questions (FAQ)

What is the d/(dy)((y^3-8)/(y^3+8)) ?
The d/(dy)((y^3-8)/(y^3+8)) is (48y^2)/((y^3+8)^2)
What is the first d/(dy)((y^3-8)/(y^3+8)) ?
The first d/(dy)((y^3-8)/(y^3+8)) is (48y^2)/((y^3+8)^2)