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Popular >

derivative of arcsin(x/5)

Solution

derivative of

arcsin (\frac{x}{5})

Solution

\frac{1}{25 - x ^{2}}

Solution steps

\frac{d}{d x} (arcsin (\frac{x}{5}))

Apply the chain rule:

\frac{1}{1 - ( \frac{x}{5} ) ^{2}} \frac{d}{d x} (\frac{x}{5})

= \frac{1}{1 - ( \frac{x}{5} ) ^{2}} \frac{d}{d x} (\frac{x}{5})

\frac{d}{d x} (\frac{x}{5}) = \frac{1}{5}

= \frac{1}{1 - ( \frac{x}{5} ) ^{2}} \cdot \frac{1}{5}

Simplify

\frac{1}{1 - ( \frac{x}{5} ) ^{2}} \cdot \frac{1}{5} : \frac{1}{25 - x ^{2}}

= \frac{1}{25 - x ^{2}}

Popular Examples

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x \to - 1 - lim (\frac{6}{x + 1})

integral of (x^2)/(x^3+5)

\int \frac{x ^{2}}{x ^{3} + 5} d x

derivative of f(t)=(cos(t))/(t^3)derivative of

f (t) = \frac{cos ( t )}{t ^{3}}

f (t) = sec (t)

sum from n=0 to infinity of (e/(6pi))^n

n = 0 \sum \infty (\frac{e}{6 π})^{n}

Frequently Asked Questions (FAQ)

What is the derivative of arcsin(x/5) ?
The derivative of arcsin(x/5) is 1/(sqrt(25-x^2))
What is the first derivative of arcsin(x/5) ?
The first derivative of arcsin(x/5) is 1/(sqrt(25-x^2))