What is the derivative of f(x)=arcsin(3x) ?

The derivative of f(x)=arcsin(3x) is 3/(sqrt(1-9x^2))

What is the first derivative of f(x)=arcsin(3x) ?

The first derivative of f(x)=arcsin(3x) is 3/(sqrt(1-9x^2))

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derivative of

f (x) = arcsin (3 x)

\frac{3}{1 - 9 x ^{2}}

Solution steps

\frac{d}{d x} (arcsin (3 x))

Apply the chain rule:

\frac{1}{1 - ( 3 x ) ^{2}} \frac{d}{d x} (3 x)

= \frac{1}{1 - ( 3 x ) ^{2}} \frac{d}{d x} (3 x)

\frac{d}{d x} (3 x) = 3

= \frac{1}{1 - ( 3 x ) ^{2}} \cdot 3

Simplify

\frac{1}{1 - ( 3 x ) ^{2}} \cdot 3 : \frac{3}{1 - 9 x ^{2}}

= \frac{3}{1 - 9 x ^{2}}

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What is the derivative of f(x)=arcsin(3x) ?
The derivative of f(x)=arcsin(3x) is 3/(sqrt(1-9x^2))
What is the first derivative of f(x)=arcsin(3x) ?
The first derivative of f(x)=arcsin(3x) is 3/(sqrt(1-9x^2))