What is the derivative of (x^2+1/(sqrt(3-x^2))) ?

The derivative of (x^2+1/(sqrt(3-x^2))) is (-x^3+7x)/((3-x^2)sqrt(3-x^2))

What is the first derivative of (x^2+1/(sqrt(3-x^2))) ?

The first derivative of (x^2+1/(sqrt(3-x^2))) is (-x^3+7x)/((3-x^2)sqrt(3-x^2))

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

\frac{- x ^{3} + 7 x}{( 3 - x ^{2} ) 3 - x ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{2 x 3 - x ^{2} - ( - \frac{x}{3 - x ^{2}} ) ( x ^{2} + 1 )}{( 3 - x ^{2} ) ^{2}} : \frac{- x ^{3} + 7 x}{( 3 - x ^{2} ) 3 - x ^{2}}

= \frac{- x ^{3} + 7 x}{( 3 - x ^{2} ) 3 - x ^{2}}

\frac{d}{d x} ((x - π) sin (x))

\frac{1}{3 x + 4}

x \to 4 lim (- \frac{3 x}{7} + \frac{8}{7})

x \to 9 - lim (81 - x^{2})

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

What is the derivative of (x^2+1/(sqrt(3-x^2))) ?
The derivative of (x^2+1/(sqrt(3-x^2))) is (-x^3+7x)/((3-x^2)sqrt(3-x^2))
What is the first derivative of (x^2+1/(sqrt(3-x^2))) ?
The first derivative of (x^2+1/(sqrt(3-x^2))) is (-x^3+7x)/((3-x^2)sqrt(3-x^2))