What is the derivative of ((x^2-6^3)/(x^2+4)) ?

The derivative of ((x^2-6^3)/(x^2+4)) is (6x(x^2-6)^2(x^2+4)-2x(x^2-6)^3)/((x^2+4)^2)

What is the first derivative of ((x^2-6^3)/(x^2+4)) ?

The first derivative of ((x^2-6^3)/(x^2+4)) is (6x(x^2-6)^2(x^2+4)-2x(x^2-6)^3)/((x^2+4)^2)

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

\frac{d ^{2}}{d x ^{2}} (x^{\frac{9}{5}} y^{7} z^{\frac{2}{7}})

y^{^{''}} - 6 y^{^{'}} + 9 y = 6 e^{3 x}

\int cos (\frac{x}{2}) d x

x \to 3 lim (4 cos (x))

x, x^{0.5}

What is the derivative of ((x^2-6^3)/(x^2+4)) ?
The derivative of ((x^2-6^3)/(x^2+4)) is (6x(x^2-6)^2(x^2+4)-2x(x^2-6)^3)/((x^2+4)^2)
What is the first derivative of ((x^2-6^3)/(x^2+4)) ?
The first derivative of ((x^2-6^3)/(x^2+4)) is (6x(x^2-6)^2(x^2+4)-2x(x^2-6)^3)/((x^2+4)^2)