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

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

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

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

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

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

Solution steps

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

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

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

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

\frac{d}{d x} (\frac{3 x}{x})

f (x) = (2)^{x}, at x = 6

y = e^{6 x} cos (π x), (0, 1)

y^{^{''}} + 14 y^{^{'}} + 28 y = 6675 e^{2 t} cos (15 t)

\frac{d}{d x} (5 x - 3)

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