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Popular Calculus >

derivative of sin(narcsin(x))

Solution

\frac{d}{d x} (sin (n arcsin (x)))

Solution

\frac{n cos ( n arcsin ( x ) )}{1 - x ^{2}}

Solution steps

\frac{d}{d x} (sin (n arcsin (x)))

Apply the chain rule:

cos (n arcsin (x)) \frac{d}{d x} (n arcsin (x))

= cos (n arcsin (x)) \frac{d}{d x} (n arcsin (x))

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

= cos (n arcsin (x)) \frac{n}{1 - x ^{2}}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{n cos ( n arcsin ( x ) )}{1 - x ^{2}}

Graph

Popular Examples

integral of (8x-5)/(\sqrt[3]{x)}

\int \frac{8 x - 5}{3 x} d x

derivative of (sec(2x)/(1+tan(2x)))

\frac{d}{d x} (\frac{sec ( 2 x )}{1 + tan ( 2 x )})

integral of cot^3(x/3)

\int cot^{3} (\frac{x}{3}) d x

integral of xln^4(x)

\int x ln^{4} (x) d x

(\partial)/(\partial x)((2x-y)/(5xy+6))

\frac{\partial}{\partial x} (\frac{2 x - y}{5 x y + 6})

Frequently Asked Questions (FAQ)

What is the derivative of sin(narcsin(x)) ?
The derivative of sin(narcsin(x)) is (ncos(narcsin(x)))/(sqrt(1-x^2))
What is the first derivative of sin(narcsin(x)) ?
The first derivative of sin(narcsin(x)) is (ncos(narcsin(x)))/(sqrt(1-x^2))