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derivative of sec(sqrt(x^2-1))

Solution

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

Solution

\frac{x sec ( x ^{2} - 1 ) tan ( x ^{2} - 1 )}{x ^{2} - 1}

Solution steps

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

Apply the chain rule:

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

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

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

= sec (x^{2} - 1) tan (x^{2} - 1) \frac{x}{x ^{2} - 1}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{x sec ( x ^{2} - 1 ) tan ( x ^{2} - 1 )}{x ^{2} - 1}

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

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(dy)/(dx)+1/(x+8)y=x^{-2}

\frac{d y}{d x} + \frac{1}{x + 8} y = x^{- 2}

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Frequently Asked Questions (FAQ)

What is the derivative of sec(sqrt(x^2-1)) ?
The derivative of sec(sqrt(x^2-1)) is (xsec(sqrt(x^2-1))tan(sqrt(x^2-1)))/(sqrt(x^2-1))
What is the first derivative of sec(sqrt(x^2-1)) ?
The first derivative of sec(sqrt(x^2-1)) is (xsec(sqrt(x^2-1))tan(sqrt(x^2-1)))/(sqrt(x^2-1))