What is the derivative of arcsin(x/8) ?

The derivative of arcsin(x/8) is 1/(sqrt(64-x^2))

What is the first derivative of arcsin(x/8) ?

The first derivative of arcsin(x/8) is 1/(sqrt(64-x^2))

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\frac{d}{d x} (arcsin (\frac{x}{8}))

\frac{1}{64 - x ^{2}}

Solution steps

\frac{d}{d x} (arcsin (\frac{x}{8}))

Apply the chain rule:

\frac{1}{1 - ( \frac{x}{8} ) ^{2}} \frac{d}{d x} (\frac{x}{8})

= \frac{1}{1 - ( \frac{x}{8} ) ^{2}} \frac{d}{d x} (\frac{x}{8})

\frac{d}{d x} (\frac{x}{8}) = \frac{1}{8}

= \frac{1}{1 - ( \frac{x}{8} ) ^{2}} \cdot \frac{1}{8}

Simplify

\frac{1}{1 - ( \frac{x}{8} ) ^{2}} \cdot \frac{1}{8} : \frac{1}{64 - x ^{2}}

= \frac{1}{64 - x ^{2}}

\frac{d y}{d x} + 5 y = 3 sin (e^{5 x})

\frac{1}{5 x}

\int \frac{1}{6 x ^{3} - 7 x ^{2} - 3 x} d x

\frac{\partial}{\partial v} (sin (u) cos (v))

y^{^{'}} = 5 y - x y

What is the derivative of arcsin(x/8) ?
The derivative of arcsin(x/8) is 1/(sqrt(64-x^2))
What is the first derivative of arcsin(x/8) ?
The first derivative of arcsin(x/8) is 1/(sqrt(64-x^2))