What is the derivative of arcsin(6/7 x) ?

The derivative of arcsin(6/7 x) is 6/(sqrt(49-36x^2))

What is the first derivative of arcsin(6/7 x) ?

The first derivative of arcsin(6/7 x) is 6/(sqrt(49-36x^2))

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derivative of

arcsin (\frac{6}{7} x)

\frac{6}{49 - 36 x ^{2}}

Solution steps

\frac{d}{d x} (arcsin (\frac{6}{7} x))

Simplify

arcsin (\frac{6}{7} x) : arcsin (\frac{6 x}{7})

= \frac{d}{d x} (arcsin (\frac{6 x}{7}))

Apply the chain rule:

\frac{1}{1 - ( \frac{6 x}{7} ) ^{2}} \frac{d}{d x} (\frac{6 x}{7})

= \frac{1}{1 - ( \frac{6 x}{7} ) ^{2}} \frac{d}{d x} (\frac{6 x}{7})

\frac{d}{d x} (\frac{6 x}{7}) = \frac{6}{7}

= \frac{1}{1 - ( \frac{6 x}{7} ) ^{2}} \cdot \frac{6}{7}

Simplify

\frac{1}{1 - ( \frac{6 x}{7} ) ^{2}} \cdot \frac{6}{7} : \frac{6}{49 - 36 x ^{2}}

= \frac{6}{49 - 36 x ^{2}}

What is the derivative of arcsin(6/7 x) ?
The derivative of arcsin(6/7 x) is 6/(sqrt(49-36x^2))
What is the first derivative of arcsin(6/7 x) ?
The first derivative of arcsin(6/7 x) is 6/(sqrt(49-36x^2))