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

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

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

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

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

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

Solution steps

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

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

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

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

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

(8 x^{2} - 13 x) e^{x}

\frac{\partial}{\partial x} ((x - y) e^{- x^{2} - y^{2}})

sin (5 t)

y^{^{''}} - y^{^{'}} - 2 y = 8 e - t

f (x) = x^{\frac{1}{x}}

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