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Popular >

derivative of arcsin(3x-4x^3)

Solution

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

Solution

- \frac{3}{- ( x + 1 ) ( x - 1 )}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (3 x - 4 x^{3}) = 3 - 12 x^{2}

= \frac{1}{1 - ( 3 x - 4 x ^{3} ) ^{2}} (3 - 12 x^{2})

Simplify

\frac{1}{1 - ( 3 x - 4 x ^{3} ) ^{2}} (3 - 12 x^{2}) : - \frac{3}{- ( x + 1 ) ( x - 1 )}

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

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Frequently Asked Questions (FAQ)

What is the derivative of arcsin(3x-4x^3) ?
The derivative of arcsin(3x-4x^3) is -3/(sqrt(-(x+1)(x-1)))
What is the first derivative of arcsin(3x-4x^3) ?
The first derivative of arcsin(3x-4x^3) is -3/(sqrt(-(x+1)(x-1)))