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differentiating sec^n x etc
Can someone please check these rules are correct for differentiating
sec^n x => n sec^(n-1) x secxtanx
cosec^n x => ncosec^(n-1) x -cosecxcotx {i am confused here, if i am supposed to minus cosecxcotx, or multiply by -(cosecxcotx)}
ncot^(n-1) x -cosec^2 x {same confusion here}
thanks
also for
cos^n x is it + or - ncos^(n-1) xsinx
because my work says it is + but for everyother time you dy/dx cos you get -sin?
sec^n x => n sec^(n-1) x secxtanx
cosec^n x => ncosec^(n-1) x -cosecxcotx {i am confused here, if i am supposed to minus cosecxcotx, or multiply by -(cosecxcotx)}
ncot^(n-1) x -cosec^2 x {same confusion here}
thanks
also for
cos^n x is it + or - ncos^(n-1) xsinx
because my work says it is + but for everyother time you dy/dx cos you get -sin?
sec^n x => n sec^(n-1) x secxtanx
That's right. Could be simplified to: n(secx)^n.tanx
cosec^n x => ncosec^(n-1) x -cosecxcotx {i am confused here, if i am supposed to minus cosecxcotx, or multiply by -(cosecxcotx)}
Multiply. It's the chain rule.
It simplifies to -n(cosecx)^n.cotx.
ncot^(n-1) x -cosec^2 x {same confusion here}
The derivative of (cotx)^n is -n(cotx)^(n-1).(cosecx)^2
cos^n x is it + or - ncos^(n-1) xsinx
It's minus.
Consider y=(cosx)^n.
y=t^n, t=cosx.
dy/dt=nt^(n-1). dt/dx=-sinx
dy/dx=dy/dt.dt/dx=-(sinx)nt^(n-1)=-n(sinx)(cosx)^(n-1).
Reply 2
thanks lots and lots, it seems the data sheet my teacher gave me to revise from is wrong in so many ways! ( 
)
i think in the exam i will use the substitution of t and figure them out the long way, remembering these shortcut rules seems confusing.
)i think in the exam i will use the substitution of t and figure them out the long way, remembering these shortcut rules seems confusing.
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