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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x}{a}) = \frac{1}{a}

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

Simplify

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

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

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

y^{2} d y + x^{3} d x = 0

f (x) = \frac{7}{x ^{2}} - 6 x^{2}, at x = 5

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

\int \frac{( 1 - x )}{e ^{x}} k d x

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