What is the derivative of arcsin(9x^5) ?

The derivative of arcsin(9x^5) is (45x^4)/(sqrt(1-81x^{10))}

What is the first derivative of arcsin(9x^5) ?

The first derivative of arcsin(9x^5) is (45x^4)/(sqrt(1-81x^{10))}

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\frac{d}{d x} (arcsin (9 x^{5}))

\frac{45 x ^{4}}{1 - 81 x ^{10}}

Solution steps

\frac{d}{d x} (arcsin (9 x^{5}))

Apply the chain rule:

\frac{1}{1 - ( 9 x ^{5} ) ^{2}} \frac{d}{d x} (9 x^{5})

= \frac{1}{1 - ( 9 x ^{5} ) ^{2}} \frac{d}{d x} (9 x^{5})

\frac{d}{d x} (9 x^{5}) = 45 x^{4}

= \frac{1}{1 - ( 9 x ^{5} ) ^{2}} \cdot 45 x^{4}

Simplify

\frac{1}{1 - ( 9 x ^{5} ) ^{2}} \cdot 45 x^{4} : \frac{45 x ^{4}}{1 - 81 x ^{10}}

= \frac{45 x ^{4}}{1 - 81 x ^{10}}

What is the derivative of arcsin(9x^5) ?
The derivative of arcsin(9x^5) is (45x^4)/(sqrt(1-81x^{10))}
What is the first derivative of arcsin(9x^5) ?
The first derivative of arcsin(9x^5) is (45x^4)/(sqrt(1-81x^{10))}