Jun 5, 2016 · To find the derivative of secant, we could either use the limit definition of the derivative (which would take a very long time) or the definition of secant itself: #secx=1/cosx# We know #d/dxcosx=-sinx# - keep that in mind because we're going to need it. Our problem is: #d/dxsecx# Since #secx=1/cosx#, we can write this as: #d/dx1/cosx#

The derivatives of \sec(x), \cot(x), and \csc(x) can be calculated by using the quotient rule of differentiation together with the identities \sec(x)=\frac{1}{\cos(x ...

Mar 7, 2018 · Define the function: # f(x)=secx # Using the limit definition of the derivative, we have: # f'(x) = lim_(h rarr 0) (f(x+h)-f(x))/h #

Feb 4, 2015 · For the second derivative of #\sec(x)#, let's derive one more time the first derivative: again, ...

Dec 11, 2014 · Let y=sec^{-1}x. by rewriting in terms of secant, => sec y=x by differentiating with respect to x, => sec y tan y cdot y'=1 by dividing by sec y tan y, => y' = 1/{sec y tan y} since sec y =x and tan x = sqrt{sec^2 y -1}=sqrt{x^2-1} => y'=1/{x sqrt{x^2-1}} Hence, d/dx(sec^{-1}x)=1/{x sqrt{x^2-1}} I hope that this was helpful.

Sep 7, 2014 · #d/dx sec(x)=sec(x)tan(x)# You could memorize this, but you can work it out too by knowing some trig properties. The trig properties we will use are: #sec (x)= 1/cos(x)# and #sin x/cos x=tan x# Deriving: #d/dx sec (x) = d/dx 1/cos(x) = (cos (x)(0) - 1 (-sin (x)))/( cos (x)cos (x))# (using the quotient rule)

Find the Derivative of y = sec 2 (x). Differentiate both sides w.r.t x using chain rule. d y d x = d d x sec 2 x = 2 sec x d d x sec x chain rule : d d x f g x = d d x f g x × d d x g ( x ) Power rule : d d x x n = n x n - 1 = 2 sec x × sec x tan x = 2 sec 2 x tan x

Jan 5, 2016 · 4sec^2 2xtan2x Use the chain rule. The first issue is the squared term. d/dx(u^2)=2u*u' d/dx(sec^2 2x)=2sec2x*d/dx(sec2x) Use chain rule again: d/dx(secu)=secutanu*u' d/dx(sec^2 2x)=2sec2x*sec2xtan2x*d/dx(2x) Since d/dx(2x)=2, d/dx(sec^2 2x)=4sec^2 2xtan2x

Oct 22, 2017 · STEP 1: # sec x = 1 / cos x # STEP 2: Use the quotient rule to find the derivative of # Sec x = 1 / cos x # # (d/dx 1 * (cos x) - d/dx cosx * (1)) / (cosx)^2 #

May 3, 2018 · -sin(x) Since sec(x) means 1/cos(x), then 1/sec(x) is cos(x) itself. And thus, its derivative is -sin(x)