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Popular >

derivative of arcsin(1/2 x)

Solution

\frac{d}{d x} (arcsin (\frac{1}{2} x))

Solution

\frac{1}{4 - x ^{2}}

Solution steps

\frac{d}{d x} (arcsin (\frac{1}{2} x))

Simplify

arcsin (\frac{1}{2} x) : arcsin (\frac{x}{2})

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x}{2}) = \frac{1}{2}

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

Simplify

\frac{1}{1 - ( \frac{x}{2} ) ^{2}} \cdot \frac{1}{2} : \frac{1}{4 - x ^{2}}

= \frac{1}{4 - x ^{2}}

Popular Examples

(\partial)/(\partial x)(arctan(x/3))

\frac{\partial}{\partial x} (arctan (\frac{x}{3}))

limit as x approaches-3+of x/(x^2-9)

x \to - 3 + lim (\frac{x}{x ^{2} - 9})

limit as x approaches 2 of (x^3-8)/(2x)

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

(\partial)/(\partial x)(xe^{xy}-2y+1)

\frac{\partial}{\partial x} (x e^{x y} - 2 y + 1)

limit as x approaches 3 of cos(1/(x-3))

x \to 3 lim (cos (\frac{1}{x - 3}))

Frequently Asked Questions (FAQ)

What is the derivative of arcsin(1/2 x) ?
The derivative of arcsin(1/2 x) is 1/(sqrt(4-x^2))
What is the first derivative of arcsin(1/2 x) ?
The first derivative of arcsin(1/2 x) is 1/(sqrt(4-x^2))