What is the derivative of ((x^2-1)^3)/(x^2+4) ?

The derivative of ((x^2-1)^3)/(x^2+4) is (6x(x^2-1)^2(x^2+4)-2x(x^2-1)^3)/((x^2+4)^2)

What is the first derivative of ((x^2-1)^3)/(x^2+4) ?

The first derivative of ((x^2-1)^3)/(x^2+4) is (6x(x^2-1)^2(x^2+4)-2x(x^2-1)^3)/((x^2+4)^2)

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derivative of

\frac{( x ^{2} - 1 ) ^{3}}{x ^{2} + 4}

\frac{6 x ( x ^{2} - 1 ) ^{2} ( x ^{2} + 4 ) - 2 x ( x ^{2} - 1 ) ^{3}}{( x ^{2} + 4 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{( x ^{2} - 1 ) ^{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} - 1 ) ^{3} ) ( x ^{2} + 4 ) - \frac{d}{d x} ( x ^{2} + 4 ) ( x ^{2} - 1 ) ^{3}}{( x ^{2} + 4 ) ^{2}}

\frac{d}{d x} ((x^{2} - 1)^{3}) = 6 x (x^{2} - 1)^{2}

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

= \frac{6 x ( x ^{2} - 1 ) ^{2} ( x ^{2} + 4 ) - 2 x ( x ^{2} - 1 ) ^{3}}{( x ^{2} + 4 ) ^{2}}

\int 3 x^{2} - 6 x + 3 d x

\int \frac{x - 1}{x + 1} d x

\frac{d}{d x} (2 (x^{2} + 5 x - 2)^{- \frac{5}{7}})

\frac{d ^{2} y}{d t ^{2}} + 9 y = 0

\frac{d}{d x} (csc^{2} (x - 2))

What is the derivative of ((x^2-1)^3)/(x^2+4) ?
The derivative of ((x^2-1)^3)/(x^2+4) is (6x(x^2-1)^2(x^2+4)-2x(x^2-1)^3)/((x^2+4)^2)
What is the first derivative of ((x^2-1)^3)/(x^2+4) ?
The first derivative of ((x^2-1)^3)/(x^2+4) is (6x(x^2-1)^2(x^2+4)-2x(x^2-1)^3)/((x^2+4)^2)