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Popular Calculus >

derivative of arcsin(x^4)

Solution

derivative of

arcsin (x^{4})

Solution

\frac{4 x ^{3}}{1 - x ^{8}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{4 x ^{3}}{1 - x ^{8}}

Graph

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Frequently Asked Questions (FAQ)

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