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

The derivative of (|x|/(sqrt(2-x^2))) is (2x)/(|x|(2-x^2)sqrt(-x^2+2))

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

The first derivative of (|x|/(sqrt(2-x^2))) is (2x)/(|x|(2-x^2)sqrt(-x^2+2))

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

\frac{2 x}{∣ x ∣ ( 2 - x ^{2} ) - x ^{2} + 2}

Solution steps

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

\frac{d}{d x} (∣ x ∣) = \frac{x}{∣ x ∣}

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

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

Simplify

\frac{\frac{x}{∣ x ∣} 2 - x ^{2} - ( - \frac{x}{2 - x ^{2}} ) ∣ x ∣}{( 2 - x ^{2} ) ^{2}} : \frac{2 x}{∣ x ∣ ( 2 - x ^{2} ) - x ^{2} + 2}

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

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