Question

If y = sec x tan x, find dy/dx​

Answer 1

Answer:

The required answer is  dy/dx = $( 1 + sin x )/ ( cos x ) ^2$

Step-by-step explanation:

Differentiation: It is the process of determining a function that returns the rate of change of one variable in relation to another. Informally, we can imagine we're following the progress of an automobile on a two-lane road with no passing lanes.

Given: $y = ( sec x + tan x )$

To find: dy/dx

We have $y = ( sec x + tan x )$

Now,

Differentiate both sides with respect to $x$

Then $dy/dx = d/dx (sec x) + d/dx (tanx)$

$d y/dx = sec x . tan x + (sec x)^2$

$dy/dx = sec x [ tan x + sec x ]$

$dy/dx = sec x [ sin x/cos x + 1/cos x ]$

$dy/dx = sec x [ (sin x + 1 ) / cos x ]$

$dy/dx = ( 1 + sin x )/ ( cos x ) ^2$

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