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

The derivative of (x^2-3/(x^3)) is (-x^2+9)/(x^4)

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

The first derivative of (x^2-3/(x^3)) is (-x^2+9)/(x^4)

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

\frac{- x ^{2} + 9}{x ^{4}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{2 x x ^{3} - 3 x ^{2} ( x ^{2} - 3 )}{( x ^{3} ) ^{2}} : \frac{- x ^{2} + 9}{x ^{4}}

= \frac{- x ^{2} + 9}{x ^{4}}

3 x^{^{'}} + 6 x = 4

\frac{r d θ}{d r} = θ^{2} + 1

f (x) = 5 - x^{2}, at x = 1

x^{2} - 7

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

What is the derivative of (x^2-3/(x^3)) ?
The derivative of (x^2-3/(x^3)) is (-x^2+9)/(x^4)
What is the first derivative of (x^2-3/(x^3)) ?
The first derivative of (x^2-3/(x^3)) is (-x^2+9)/(x^4)