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

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

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

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

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derivative of

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{e ^{x} - e ^{- x}}{2}

\frac{d}{d x} (ln (e^{3 x^{2}} \cdot 4^{5 x}))

\frac{\partial}{\partial x} ((1 + x y)^{\frac{3}{2}})

x \to \infty lim (e^{- 4 x} cos (4 x))

\int_{0}^{10} x - 5 d x

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