What is the derivative of (|x|)/(sqrt(5-x^2)) ?

The derivative of (|x|)/(sqrt(5-x^2)) is (5x)/(|x|(5-x^2)sqrt(-x^2+5))

What is the first derivative of (|x|)/(sqrt(5-x^2)) ?

The first derivative of (|x|)/(sqrt(5-x^2)) is (5x)/(|x|(5-x^2)sqrt(-x^2+5))

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derivative of

\frac{∣ x ∣}{5 - x ^{2}}

\frac{5 x}{∣ x ∣ ( 5 - x ^{2} ) - x ^{2} + 5}

Solution steps

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

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( ∣ x ∣ ) 5 - x ^{2} - \frac{d}{d x} ( 5 - x ^{2} ) ∣ x ∣}{( 5 - x ^{2} ) ^{2}}

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

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

= \frac{\frac{x}{∣ x ∣} 5 - x ^{2} - ( - \frac{x}{5 - x ^{2}} ) ∣ x ∣}{( 5 - x ^{2} ) ^{2}}

Simplify

\frac{\frac{x}{∣ x ∣} 5 - x ^{2} - ( - \frac{x}{5 - x ^{2}} ) ∣ x ∣}{( 5 - x ^{2} ) ^{2}} : \frac{5 x}{∣ x ∣ ( 5 - x ^{2} ) - x ^{2} + 5}

= \frac{5 x}{∣ x ∣ ( 5 - x ^{2} ) - x ^{2} + 5}

x^{2} y d x - (x^{3} + y^{3}) d y = 0

f (x) = (2 x^{2} + 3) (5 x - 4)

f (x) = \frac{e ^{x}}{x}

x \to - 3 lim (\frac{x ^{3} + 8}{x + 2})

e^{2 - 5 x}

What is the derivative of (|x|)/(sqrt(5-x^2)) ?
The derivative of (|x|)/(sqrt(5-x^2)) is (5x)/(|x|(5-x^2)sqrt(-x^2+5))
What is the first derivative of (|x|)/(sqrt(5-x^2)) ?
The first derivative of (|x|)/(sqrt(5-x^2)) is (5x)/(|x|(5-x^2)sqrt(-x^2+5))