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Popular >

derivative of arcsin(x/4)

Solution

\frac{d}{d x} (arcsin (\frac{x}{4}))

Solution

\frac{1}{16 - x ^{2}}

Solution steps

\frac{d}{d x} (arcsin (\frac{x}{4}))

Apply the chain rule:

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

= \frac{1}{1 - ( \frac{x}{4} ) ^{2}} \frac{d}{d x} (\frac{x}{4})

\frac{d}{d x} (\frac{x}{4}) = \frac{1}{4}

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

Simplify

\frac{1}{1 - ( \frac{x}{4} ) ^{2}} \cdot \frac{1}{4} : \frac{1}{16 - x ^{2}}

= \frac{1}{16 - x ^{2}}

Popular Examples

derivative of tan^4(3x)

\frac{d}{d x} (tan^{4} (3 x))

integral of y^3e^{-y}

\int y^{3} e^{- y} d y

integral of-14/15*(x-30)+14

\int - \frac{14}{15} \cdot (x - 30) + 14 d x

(dy)/(dx)=e^{2x-1}y^2

\frac{d y}{d x} = e^{2 x - 1} y^{2}

integral of (sqrt(x^2+25))/(x^2)

\int \frac{x ^{2} + 25}{x ^{2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of arcsin(x/4) ?
The derivative of arcsin(x/4) is 1/(sqrt(16-x^2))
What is the first derivative of arcsin(x/4) ?
The first derivative of arcsin(x/4) is 1/(sqrt(16-x^2))