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Popular >

derivative of arcsin(x^{100})

Solution

\frac{d}{d x} (arcsin (x^{100}))

Solution

\frac{100 x ^{99}}{1 - x ^{200}}

Solution steps

\frac{d}{d x} (arcsin (x^{100}))

Apply the chain rule:

\frac{1}{1 - ( x ^{100} ) ^{2}} \frac{d}{d x} (x^{100})

= \frac{1}{1 - ( x ^{100} ) ^{2}} \frac{d}{d x} (x^{100})

\frac{d}{d x} (x^{100}) = 100 x^{99}

= \frac{1}{1 - ( x ^{100} ) ^{2}} \cdot 100 x^{99}

Simplify

\frac{1}{1 - ( x ^{100} ) ^{2}} \cdot 100 x^{99} : \frac{100 x ^{99}}{1 - x ^{200}}

= \frac{100 x ^{99}}{1 - x ^{200}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of arcsin(x^{100}) ?
The derivative of arcsin(x^{100}) is (100x^{99})/(sqrt(1-x^{200))}
What is the first derivative of arcsin(x^{100}) ?
The first derivative of arcsin(x^{100}) is (100x^{99})/(sqrt(1-x^{200))}