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Popular >

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}}

Popular Examples

derivative of f(x)= 7/x derivative of

f (x) = \frac{7}{x}

limit as x approaches infinity of ((x-3)/(x-4))^{-x}

x \to \infty lim ((\frac{x - 3}{x - 4})^{- x})

derivative of ln(sinh(5x))

\frac{d}{d x} (ln (sinh (5 x)))

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y = (3 x - 2 x^{2})^{3}

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\frac{9 + 6 x}{7 - 4 x}

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))