What is the derivative of arcsin(x^9) ?

The derivative of arcsin(x^9) is (9x^8)/(sqrt(1-x^{18))}

What is the first derivative of arcsin(x^9) ?

The first derivative of arcsin(x^9) is (9x^8)/(sqrt(1-x^{18))}

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\frac{d}{d x} (arcsin (x^{9}))

\frac{9 x ^{8}}{1 - x ^{18}}

Solution steps

\frac{d}{d x} (arcsin (x^{9}))

Apply the chain rule:

\frac{1}{1 - ( x ^{9} ) ^{2}} \frac{d}{d x} (x^{9})

= \frac{1}{1 - ( x ^{9} ) ^{2}} \frac{d}{d x} (x^{9})

\frac{d}{d x} (x^{9}) = 9 x^{8}

= \frac{1}{1 - ( x ^{9} ) ^{2}} \cdot 9 x^{8}

Simplify

\frac{1}{1 - ( x ^{9} ) ^{2}} \cdot 9 x^{8} : \frac{9 x ^{8}}{1 - x ^{18}}

= \frac{9 x ^{8}}{1 - x ^{18}}

What is the derivative of arcsin(x^9) ?
The derivative of arcsin(x^9) is (9x^8)/(sqrt(1-x^{18))}
What is the first derivative of arcsin(x^9) ?
The first derivative of arcsin(x^9) is (9x^8)/(sqrt(1-x^{18))}