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

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

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

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

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

\frac{2 a ^{2}}{( a ^{2} - x ^{2} ) a ^{2} - x ^{2}}

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

2 \cdot \frac{1 \cdot a ^{2} - x ^{2} - ( - \frac{x}{a ^{2} - x ^{2}} ) x}{( a ^{2} - x ^{2} ) ^{2}} : \frac{2 a ^{2}}{( a ^{2} - x ^{2} ) a ^{2} - x ^{2}}

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

n = 1 \sum \infty \frac{1}{4 n ^{2} + 7}

y^{^{''}} + a y = 0, y (0) = 1, y (1) = 0

(8.2) (9.3)

x \to - 2 lim (\frac{1 + x}{x ^{3} + 8})

3 x 3 x^{2} + 1

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