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Popular >

derivative of arcsec(4x)

Solution

derivative of

arcsec (4 x)

Solution

\frac{1}{x ^{2} 16 x ^{2} - 1}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{( 4 x ) ^{2} ( 4 x ) ^{2} - 1} \cdot 4 : \frac{1}{x ^{2} 16 x ^{2} - 1}

= \frac{1}{x ^{2} 16 x ^{2} - 1}

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\int \frac{( x ^{2} - 1 )}{x ^{3} + x} d x

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Frequently Asked Questions (FAQ)

What is the derivative of arcsec(4x) ?
The derivative of arcsec(4x) is 1/(sqrt(x^2)\sqrt{16x^2-1)}
What is the first derivative of arcsec(4x) ?
The first derivative of arcsec(4x) is 1/(sqrt(x^2)\sqrt{16x^2-1)}