What is the derivative of this function $y=sec^-1(5x)$ ?

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Answer 1 · 2018-05-05T12:49:51

$(dy)/(dx)=1/(|x|sqrt(25x^2-1))$

We know that,

$color(red)(d/(dt)(sec^-1t)=1/(|t|sqrt(t^2-1))$

Here,

$y=sec^-1(5x)$

Let.

$y=sec^-1u ,where, u=5x$

$=>(dy)/(du)=1/(|u|sqrt(u^2-1)) and (du)/(dx)=5$

$"Using "color(blue)"Integration by Parts"$

$color(blue)((dy)/(dx)=(dy)/(du)*(du)/(dx)$

So, $(dy)/(dx)=1/(|u|sqrt(u^2-1))xx5$
$(dy)/(dx)=5/(|5x|sqrt(25x^2-1))$

$(dy)/(dx)=1/(|x|sqrt(25x^2-1))$

What is the derivative of this function y=sec^-1(5x)y=sec^-1(5x)?