What is the derivative of (x^3+1)/(x^3+8) ?

The derivative of (x^3+1)/(x^3+8) is (21x^2)/((x^3+8)^2)

What is the first derivative of (x^3+1)/(x^3+8) ?

The first derivative of (x^3+1)/(x^3+8) is (21x^2)/((x^3+8)^2)

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derivative of

\frac{x ^{3} + 1}{x ^{3} + 8}

\frac{21 x ^{2}}{( x ^{3} + 8 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{3} + 1}{x ^{3} + 8})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{3} + 1 ) ( x ^{3} + 8 ) - \frac{d}{d x} ( x ^{3} + 8 ) ( x ^{3} + 1 )}{( x ^{3} + 8 ) ^{2}}

\frac{d}{d x} (x^{3} + 1) = 3 x^{2}

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

= \frac{3 x ^{2} ( x ^{3} + 8 ) - 3 x ^{2} ( x ^{3} + 1 )}{( x ^{3} + 8 ) ^{2}}

Expand

3 x^{2} (x^{3} + 8) - 3 x^{2} (x^{3} + 1) : 21 x^{2}

= \frac{21 x ^{2}}{( x ^{3} + 8 ) ^{2}}

\frac{d}{d q} (200 - 5 q)

sin^{2} (3 x + 4)

f (x) - 7 x + 6

e^{6} x

y = \frac{( x + 1 )}{( x - 1 )}

What is the derivative of (x^3+1)/(x^3+8) ?
The derivative of (x^3+1)/(x^3+8) is (21x^2)/((x^3+8)^2)
What is the first derivative of (x^3+1)/(x^3+8) ?
The first derivative of (x^3+1)/(x^3+8) is (21x^2)/((x^3+8)^2)