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Popular >

derivative of y=arcsin(x/6)

Solution

derivative of

y = arcsin (\frac{x}{6})

Solution

\frac{1}{36 - x ^{2}}

Solution steps

\frac{d}{d x} (arcsin (\frac{x}{6}))

Apply the chain rule:

\frac{1}{1 - ( \frac{x}{6} ) ^{2}} \frac{d}{d x} (\frac{x}{6})

= \frac{1}{1 - ( \frac{x}{6} ) ^{2}} \frac{d}{d x} (\frac{x}{6})

\frac{d}{d x} (\frac{x}{6}) = \frac{1}{6}

= \frac{1}{1 - ( \frac{x}{6} ) ^{2}} \cdot \frac{1}{6}

Simplify

\frac{1}{1 - ( \frac{x}{6} ) ^{2}} \cdot \frac{1}{6} : \frac{1}{36 - x ^{2}}

= \frac{1}{36 - x ^{2}}

Popular Examples

tangent of f(x)=x^2+6 tangent of

f (x) = x^{2} + 6

integral from 0 to 1 of 36pi(x^2-x^{10})

\int_{0}^{1} 36 π (x^{2} - x^{10}) d x

limit as x approaches 0 of 1-x

x \to 0 lim (1 - x)

integral of 9/(35sin(x)-12cos(x))

\int \frac{9}{35 sin ( x ) - 12 cos ( x )} d x

integral of (x+1)(x^2+2x+5)^{12}

\int (x + 1) (x^{2} + 2 x + 5)^{12} d x

Frequently Asked Questions (FAQ)

What is the derivative of y=arcsin(x/6) ?
The derivative of y=arcsin(x/6) is 1/(sqrt(36-x^2))
What is the first derivative of y=arcsin(x/6) ?
The first derivative of y=arcsin(x/6) is 1/(sqrt(36-x^2))