What is the derivative of arcsin(3x+1) ?

The derivative of arcsin(3x+1) is 3/(sqrt(-9x^2-6x))

What is the first derivative of arcsin(3x+1) ?

The first derivative of arcsin(3x+1) is 3/(sqrt(-9x^2-6x))

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\frac{d}{d x} (arcsin (3 x + 1))

\frac{3}{- 9 x ^{2} - 6 x}

Solution steps

\frac{d}{d x} (arcsin (3 x + 1))

Apply the chain rule:

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

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

\frac{d}{d x} (3 x + 1) = 3

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

Simplify

\frac{1}{1 - ( 3 x + 1 ) ^{2}} \cdot 3 : \frac{3}{- 9 x ^{2} - 6 x}

= \frac{3}{- 9 x ^{2} - 6 x}

What is the derivative of arcsin(3x+1) ?
The derivative of arcsin(3x+1) is 3/(sqrt(-9x^2-6x))
What is the first derivative of arcsin(3x+1) ?
The first derivative of arcsin(3x+1) is 3/(sqrt(-9x^2-6x))