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Popular Calculus >

derivative of arcsin(3x^2)

Solution

\frac{d}{d x} (arcsin (3 x^{2}))

Solution

\frac{6 x}{1 - 9 x ^{4}}

Solution steps

\frac{d}{d x} (arcsin (3 x^{2}))

Apply the chain rule:

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

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

\frac{d}{d x} (3 x^{2}) = 6 x

= \frac{1}{1 - ( 3 x ^{2} ) ^{2}} \cdot 6 x

Simplify

\frac{1}{1 - ( 3 x ^{2} ) ^{2}} \cdot 6 x : \frac{6 x}{1 - 9 x ^{4}}

= \frac{6 x}{1 - 9 x ^{4}}

Graph

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x \to b lim (\frac{x - b}{x - b})

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x \to 1 lim (cos (\frac{1}{x - 1}))

Frequently Asked Questions (FAQ)

What is the derivative of arcsin(3x^2) ?
The derivative of arcsin(3x^2) is (6x)/(sqrt(1-9x^4))
What is the first derivative of arcsin(3x^2) ?
The first derivative of arcsin(3x^2) is (6x)/(sqrt(1-9x^4))