What is the derivative of arcsin(4-3x) ?

The derivative of arcsin(4-3x) is -3/(sqrt(-9x^2+24x-15))

What is the first derivative of arcsin(4-3x) ?

The first derivative of arcsin(4-3x) is -3/(sqrt(-9x^2+24x-15))

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\frac{d}{d x} (arcsin (4 - 3 x))

- \frac{3}{- 9 x ^{2} + 24 x - 15}

Solution steps

\frac{d}{d x} (arcsin (4 - 3 x))

Apply the chain rule:

\frac{1}{1 - ( 4 - 3 x ) ^{2}} \frac{d}{d x} (4 - 3 x)

= \frac{1}{1 - ( 4 - 3 x ) ^{2}} \frac{d}{d x} (4 - 3 x)

\frac{d}{d x} (4 - 3 x) = - 3

= \frac{1}{1 - ( 4 - 3 x ) ^{2}} (- 3)

Simplify

\frac{1}{1 - ( 4 - 3 x ) ^{2}} (- 3) : - \frac{3}{- 9 x ^{2} + 24 x - 15}

= - \frac{3}{- 9 x ^{2} + 24 x - 15}

What is the derivative of arcsin(4-3x) ?
The derivative of arcsin(4-3x) is -3/(sqrt(-9x^2+24x-15))
What is the first derivative of arcsin(4-3x) ?
The first derivative of arcsin(4-3x) is -3/(sqrt(-9x^2+24x-15))