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

The derivative of (4-x^2)/(x^3) is -(-x^2+12)/(x^4)

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

The first derivative of (4-x^2)/(x^3) is -(-x^2+12)/(x^4)

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derivative of

\frac{4 - x ^{2}}{x ^{3}}

- \frac{- x ^{2} + 12}{x ^{4}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{( - 2 x ) x ^{3} - 3 x ^{2} ( 4 - x ^{2} )}{( x ^{3} ) ^{2}} : - \frac{- x ^{2} + 12}{x ^{4}}

= - \frac{- x ^{2} + 12}{x ^{4}}

\frac{d}{d x} (sin (x) - x sin (y))

x \to 4 lim (\frac{2 x + 1}{3 x + 3})

\frac{d y}{d x} = \frac{e ^{x}}{y}

\int_{- \infty}^{18} x e^{\frac{x}{9}} d x

\frac{d}{d x} ((x^{2} - 10 x + 9) 25 - x^{2})

What is the derivative of (4-x^2)/(x^3) ?
The derivative of (4-x^2)/(x^3) is -(-x^2+12)/(x^4)
What is the first derivative of (4-x^2)/(x^3) ?
The first derivative of (4-x^2)/(x^3) is -(-x^2+12)/(x^4)