Question #306133

Find the dy/dx and simply the result, if possible



a. y=√x-1/√x


b. y=x²+π²+xπ


c.y=x² sec x


d.y=sinx-1/cosx


e.y=1/ex+2

1
Expert's answer
2022-03-07T11:08:03-0500

a.


y=(x1x)=12x+12xxy'=(\sqrt{x}-\dfrac{1}{\sqrt{x}})'=\dfrac{1}{2\sqrt{x}}+\dfrac{1}{2x\sqrt{x}}

=x+12xx=x(x+1)2x2=\dfrac{x+1}{2x\sqrt{x}}=\dfrac{\sqrt{x}(x+1)}{2x^2}

b.


y=(x2+π2+xπ)=2x+πy'=(x^2+\pi^2+x\pi)'=2x+\pi

c.


y=(x2secx)=2xsecx+x2(1cos2x)(sinx)y'=(x^2\sec x)'=2x\sec x+x^2(-\dfrac{1}{\cos ^2 x})(-\sin x)

=2xsecx+x2secxtanx=2x\sec x+x^2\sec x\tan x

d.


y=(sinx1cosx)=cosx(1cos2x)(sinx)y'=(\sin x-\dfrac{1}{\cos x})'=\cos x-(-\dfrac{1}{\cos ^2 x})(-\sin x)

=cosxtanxcosx=\cos x-\dfrac{\tan x}{\cos x}

e.


y=1ex+2=ex(ex+2)2y'=\dfrac{1}{e^x+2}=-\dfrac{e^x}{(e^x+2)^2}



Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS