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Popular >

derivative of arcsec(3x+2)

Solution

\frac{d}{d x} (arcsec (3 x + 2))

Solution

\frac{3}{( 3 x + 2 ) 9 x ^{2} + 12 x + 3}

Solution steps

\frac{d}{d x} (arcsec (3 x + 2))

Apply the chain rule:

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

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

\frac{d}{d x} (3 x + 2) = 3

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

Simplify

\frac{1}{( 3 x + 2 ) ^{2} ( 3 x + 2 ) ^{2} - 1} \cdot 3 : \frac{3}{( 3 x + 2 ) 9 x ^{2} + 12 x + 3}

= \frac{3}{( 3 x + 2 ) 9 x ^{2} + 12 x + 3}

Popular Examples

limit as x approaches (7pi)/2-of sec(x)

x \to \frac{7 π}{2} - lim (sec (x))

tangent of f(x)=(2x)/(3-4x^3),\at x= 1/2 tangent of

f (x) = \frac{2 x}{3 - 4 x ^{3}}, at x = \frac{1}{2}

(\partial)/(\partial x)(2/(1-3x^3))

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

(dy)/(dx)=xy+12x

\frac{d y}{d x} = x y + 12 x

derivative of y= 1/(sqrt(1+x^2))derivative of

y = \frac{1}{1 + x ^{2}}

Frequently Asked Questions (FAQ)

What is the derivative of arcsec(3x+2) ?
The derivative of arcsec(3x+2) is 3/((3x+2)sqrt(9x^2+12x+3))
What is the first derivative of arcsec(3x+2) ?
The first derivative of arcsec(3x+2) is 3/((3x+2)sqrt(9x^2+12x+3))