What is the derivative of arcsec(3x) ?

The derivative of arcsec(3x) is 1/(xsqrt(9x^2-1))

What is the first derivative of arcsec(3x) ?

The first derivative of arcsec(3x) is 1/(xsqrt(9x^2-1))

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\frac{d}{d x} (arcsec (3 x))

\frac{1}{x 9 x ^{2} - 1}

Solution steps

\frac{d}{d x} (arcsec (3 x))

Apply the chain rule:

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

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

\frac{d}{d x} (3 x) = 3

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

Simplify

\frac{1}{( 3 x ) ^{2} ( 3 x ) ^{2} - 1} \cdot 3 : \frac{1}{x 9 x ^{2} - 1}

= \frac{1}{x 9 x ^{2} - 1}

\int 5 x^{2} - \frac{4}{x} + a d x

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

\int (5 z^{2} - 3)^{3} z d z

\frac{\partial}{\partial x} (e^{7 y} sin (- 7 x))

\frac{d}{d x} (\frac{1}{arctan ( x )})

What is the derivative of arcsec(3x) ?
The derivative of arcsec(3x) is 1/(xsqrt(9x^2-1))
What is the first derivative of arcsec(3x) ?
The first derivative of arcsec(3x) is 1/(xsqrt(9x^2-1))