What is the derivative of arcsin(9x^4) ?

The derivative of arcsin(9x^4) is (36x^3)/(sqrt(1-81x^8))

What is the first derivative of arcsin(9x^4) ?

The first derivative of arcsin(9x^4) is (36x^3)/(sqrt(1-81x^8))

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\frac{d}{d x} (arcsin (9 x^{4}))

\frac{36 x ^{3}}{1 - 81 x ^{8}}

Solution steps

\frac{d}{d x} (arcsin (9 x^{4}))

Apply the chain rule:

\frac{1}{1 - ( 9 x ^{4} ) ^{2}} \frac{d}{d x} (9 x^{4})

= \frac{1}{1 - ( 9 x ^{4} ) ^{2}} \frac{d}{d x} (9 x^{4})

\frac{d}{d x} (9 x^{4}) = 36 x^{3}

= \frac{1}{1 - ( 9 x ^{4} ) ^{2}} \cdot 36 x^{3}

Simplify

\frac{1}{1 - ( 9 x ^{4} ) ^{2}} \cdot 36 x^{3} : \frac{36 x ^{3}}{1 - 81 x ^{8}}

= \frac{36 x ^{3}}{1 - 81 x ^{8}}

What is the derivative of arcsin(9x^4) ?
The derivative of arcsin(9x^4) is (36x^3)/(sqrt(1-81x^8))
What is the first derivative of arcsin(9x^4) ?
The first derivative of arcsin(9x^4) is (36x^3)/(sqrt(1-81x^8))