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Popular Calculus >

derivative of arcsec(5x^4)

Solution

\frac{d}{d x} (arcsec (5 x^{4}))

Solution

\frac{4}{x 25 x ^{8} - 1}

Solution steps

\frac{d}{d x} (arcsec (5 x^{4}))

Apply the chain rule:

\frac{1}{( 5 x ^{4} ) ^{2} ( 5 x ^{4} ) ^{2} - 1} \frac{d}{d x} (5 x^{4})

= \frac{1}{( 5 x ^{4} ) ^{2} ( 5 x ^{4} ) ^{2} - 1} \frac{d}{d x} (5 x^{4})

\frac{d}{d x} (5 x^{4}) = 20 x^{3}

= \frac{1}{( 5 x ^{4} ) ^{2} ( 5 x ^{4} ) ^{2} - 1} \cdot 20 x^{3}

Simplify

\frac{1}{( 5 x ^{4} ) ^{2} ( 5 x ^{4} ) ^{2} - 1} \cdot 20 x^{3} : \frac{4}{x 25 x ^{8} - 1}

= \frac{4}{x 25 x ^{8} - 1}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of arcsec(5x^4) ?
The derivative of arcsec(5x^4) is 4/(xsqrt(25x^8-1))
What is the first derivative of arcsec(5x^4) ?
The first derivative of arcsec(5x^4) is 4/(xsqrt(25x^8-1))