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Popular Calculus >

derivative of arcsin(x/8)

Solution

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

Solution

\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}}

Graph

Popular Examples

(dy)/(dx)+5y=3sin(e^{5x})

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

derivative of 1/(5x)

d er i v a t i v e \frac{1}{5 x}

integral of 1/(6x^3-7x^2-3x)

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

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

y^{''}+8y^'+25y=-208*sin(3x)

y^{^{''}} + 8 y^{^{'}} + 25 y = - 208 \cdot sin (3 x)

Frequently Asked Questions (FAQ)

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))