What is the derivative of ((x^2-5^3)/((x^2+4)^2)) ?

The derivative of ((x^2-5^3)/((x^2+4)^2)) is (2x(x^2-5)^2(x^2+22))/((x^2+4)^3)

What is the first derivative of ((x^2-5^3)/((x^2+4)^2)) ?

The first derivative of ((x^2-5^3)/((x^2+4)^2)) is (2x(x^2-5)^2(x^2+22))/((x^2+4)^3)

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\frac{d}{d x} (\frac{( x ^{2} - 5 ) ^{3}}{( x ^{2} + 4 ) ^{2}})

\frac{2 x ( x ^{2} - 5 ) ^{2} ( x ^{2} + 22 )}{( x ^{2} + 4 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{( x ^{2} - 5 ) ^{3}}{( x ^{2} + 4 ) ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( ( x ^{2} - 5 ) ^{3} ) ( x ^{2} + 4 ) ^{2} - \frac{d}{d x} ( ( x ^{2} + 4 ) ^{2} ) ( x ^{2} - 5 ) ^{3}}{( ( x ^{2} + 4 ) ^{2} ) ^{2}}

\frac{d}{d x} ((x^{2} - 5)^{3}) = 6 x (x^{2} - 5)^{2}

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

= \frac{6 x ( x ^{2} - 5 ) ^{2} ( x ^{2} + 4 ) ^{2} - 4 x ( x ^{2} + 4 ) ( x ^{2} - 5 ) ^{3}}{( ( x ^{2} + 4 ) ^{2} ) ^{2}}

Simplify

\frac{6 x ( x ^{2} - 5 ) ^{2} ( x ^{2} + 4 ) ^{2} - 4 x ( x ^{2} + 4 ) ( x ^{2} - 5 ) ^{3}}{( ( x ^{2} + 4 ) ^{2} ) ^{2}} : \frac{2 x ( x ^{2} - 5 ) ^{2} ( x ^{2} + 22 )}{( x ^{2} + 4 ) ^{3}}

= \frac{2 x ( x ^{2} - 5 ) ^{2} ( x ^{2} + 22 )}{( x ^{2} + 4 ) ^{3}}

x y y^{^{'}} + 1 + x^{2} + y^{2} = 0

n = 0 \sum \infty arctan (n^{2})

x^{^{''}} = x^{^{'}}

f (x) = 2 x - 1, at x = 5

\int_{0}^{1} 11 cos (x^{2}) d x

What is the derivative of ((x^2-5^3)/((x^2+4)^2)) ?
The derivative of ((x^2-5^3)/((x^2+4)^2)) is (2x(x^2-5)^2(x^2+22))/((x^2+4)^3)
What is the first derivative of ((x^2-5^3)/((x^2+4)^2)) ?
The first derivative of ((x^2-5^3)/((x^2+4)^2)) is (2x(x^2-5)^2(x^2+22))/((x^2+4)^3)