What is the derivative of arcsin(6x) ?

The derivative of arcsin(6x) is 6/(sqrt(1-36x^2))

What is the first derivative of arcsin(6x) ?

The first derivative of arcsin(6x) is 6/(sqrt(1-36x^2))

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

\frac{6}{1 - 36 x ^{2}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{6}{1 - 36 x ^{2}}

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