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

The derivative of ((x^2-5)^3)/(x^2+2) is (6x(x^2-5)^2(x^2+2)-2x(x^2-5)^3)/((x^2+2)^2)

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

The first derivative of ((x^2-5)^3)/(x^2+2) is (6x(x^2-5)^2(x^2+2)-2x(x^2-5)^3)/((x^2+2)^2)

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derivative of

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

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

Solution steps

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

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

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

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

x \to 5 lim (ln (x^{2} - 25))

\int 5 e^{x} - cos (x) + 3 x^{2} - \frac{1}{x} d x

\int \frac{1}{x 36 x ^{2} - 4} d x

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

6 \cdot 6^{t} + 2 \cdot 2 t

What is the derivative of ((x^2-5)^3)/(x^2+2) ?
The derivative of ((x^2-5)^3)/(x^2+2) is (6x(x^2-5)^2(x^2+2)-2x(x^2-5)^3)/((x^2+2)^2)
What is the first derivative of ((x^2-5)^3)/(x^2+2) ?
The first derivative of ((x^2-5)^3)/(x^2+2) is (6x(x^2-5)^2(x^2+2)-2x(x^2-5)^3)/((x^2+2)^2)