What is the derivative of arcsin(x^3) ?

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

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

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

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derivative of

arcsin (x^{3})

\frac{3 x ^{2}}{1 - x ^{6}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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