What is the derivative of f(x)=x^3(x^2+4)^{-2} ?

The derivative of f(x)=x^3(x^2+4)^{-2} is (-x^4+12x^2)/((x^2+4)^3)

What is the first derivative of f(x)=x^3(x^2+4)^{-2} ?

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

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derivative of

f (x) = x^{3} (x^{2} + 4)^{- 2}

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{3}, g = (x^{2} + 4)^{- 2}

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

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

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

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

Simplify

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

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

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

\int \frac{x ^{3} - 1}{x ^{4} - 4 x + 1} d x

\frac{d}{d x} (- 4 sec^{2} (x) + 6 sec^{4} (x))

x \to 3 lim (- 3 x - 7)

\frac{d}{d x} (\frac{5}{3 x} - \frac{6}{2 ^{x}})

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