What is the derivative of f(x)=arcsec(5x) ?

The derivative of f(x)=arcsec(5x) is 1/(sqrt(x^2)\sqrt{25x^2-1)}

What is the first derivative of f(x)=arcsec(5x) ?

The first derivative of f(x)=arcsec(5x) is 1/(sqrt(x^2)\sqrt{25x^2-1)}

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derivative of

f (x) = arcsec (5 x)

\frac{1}{x ^{2} 25 x ^{2} - 1}

Solution steps

\frac{d}{d x} (arcsec (5 x))

Apply the chain rule:

\frac{1}{( 5 x ) ^{2} ( 5 x ) ^{2} - 1} \frac{d}{d x} (5 x)

= \frac{1}{( 5 x ) ^{2} ( 5 x ) ^{2} - 1} \frac{d}{d x} (5 x)

\frac{d}{d x} (5 x) = 5

= \frac{1}{( 5 x ) ^{2} ( 5 x ) ^{2} - 1} \cdot 5

Simplify

\frac{1}{( 5 x ) ^{2} ( 5 x ) ^{2} - 1} \cdot 5 : \frac{1}{x ^{2} 25 x ^{2} - 1}

= \frac{1}{x ^{2} 25 x ^{2} - 1}

\int x os (2 x) d x

\frac{d}{d x} (a sin (b x + c) + d)

\int 5 e^{a x} d x

\int_{0}^{6} (6 - x) d x

\frac{d y}{d x}, (5 x - y)^{2} - 5 y = 2

What is the derivative of f(x)=arcsec(5x) ?
The derivative of f(x)=arcsec(5x) is 1/(sqrt(x^2)\sqrt{25x^2-1)}
What is the first derivative of f(x)=arcsec(5x) ?
The first derivative of f(x)=arcsec(5x) is 1/(sqrt(x^2)\sqrt{25x^2-1)}