What is the derivative of f(x)=arcsin(6x+1) ?

The derivative of f(x)=arcsin(6x+1) is 6/(sqrt(-36x^2-12x))

What is the first derivative of f(x)=arcsin(6x+1) ?

The first derivative of f(x)=arcsin(6x+1) is 6/(sqrt(-36x^2-12x))

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derivative of

f (x) = arcsin (6 x + 1)

\frac{6}{- 36 x ^{2} - 12 x}

Solution steps

\frac{d}{d x} (arcsin (6 x + 1))

Apply the chain rule:

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

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

\frac{d}{d x} (6 x + 1) = 6

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

Simplify

\frac{1}{1 - ( 6 x + 1 ) ^{2}} \cdot 6 : \frac{6}{- 36 x ^{2} - 12 x}

= \frac{6}{- 36 x ^{2} - 12 x}

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4 x - \frac{3}{x ^{6}}

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What is the derivative of f(x)=arcsin(6x+1) ?
The derivative of f(x)=arcsin(6x+1) is 6/(sqrt(-36x^2-12x))
What is the first derivative of f(x)=arcsin(6x+1) ?
The first derivative of f(x)=arcsin(6x+1) is 6/(sqrt(-36x^2-12x))