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Popular >

derivative of f(x)=arcsec(x+2)

Solution

derivative of

f (x) = arcsec (x + 2)

Solution

\frac{1}{( x + 2 ) ^{2} x ^{2} + 4 x + 3}

Solution steps

\frac{d}{d x} (arcsec (x + 2))

Apply the chain rule:

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

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

\frac{d}{d x} (x + 2) = 1

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

Simplify

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

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

Popular Examples

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x 6^{x}

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\frac{\partial}{\partial x} (\frac{1}{x + 3})

limit as x approaches 0 of |x^2-1|

x \to 0 lim (x^{2} - 1)

(\partial)/(\partial x)(21xye^{-x^2-y^2})

\frac{\partial}{\partial x} (21 x y e^{- x^{2} - y^{2}})

integral of e^{5x}sqrt(e^{5x)+4}

\int e^{5 x} e^{5 x} + 4 d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=arcsec(x+2) ?
The derivative of f(x)=arcsec(x+2) is 1/(sqrt((x+2)^2)\sqrt{x^2+4x+3)}
What is the first derivative of f(x)=arcsec(x+2) ?
The first derivative of f(x)=arcsec(x+2) is 1/(sqrt((x+2)^2)\sqrt{x^2+4x+3)}