What is the derivative of 2arcsec(sqrt(x)) ?

The derivative of 2arcsec(sqrt(x)) is 1/(xsqrt(x-1))

What is the first derivative of 2arcsec(sqrt(x)) ?

The first derivative of 2arcsec(sqrt(x)) is 1/(xsqrt(x-1))

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

\frac{1}{x x - 1}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{x x - 1}

\int e^{5 x} cos (7 x) d x

(3, 8), (7, - 7)

x \to 3 + lim (1 - x)

\int_{1}^{4} 2 π x (e^{x} - ln (x)) d x

(4 arccos (1 - x^{2}))^{^{'}}

What is the derivative of 2arcsec(sqrt(x)) ?
The derivative of 2arcsec(sqrt(x)) is 1/(xsqrt(x-1))
What is the first derivative of 2arcsec(sqrt(x)) ?
The first derivative of 2arcsec(sqrt(x)) is 1/(xsqrt(x-1))