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Vahe10
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#1
Ive just got theses two problems:
help wud be much appreciated:
1) e^2x + e^2y = xy
Find dy/dx.
2) y= 1/cosx
show that dy/dx = secx tanx
Thanx.
help wud be much appreciated:
1) e^2x + e^2y = xy
Find dy/dx.
2) y= 1/cosx
show that dy/dx = secx tanx
Thanx.
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Jesus09
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#2
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#2
(Original post by Vahe10)
Ive just got theses two problems:
help wud be much appreciated:
1) e^2x + e^2y = xy
Find dy/dx.
2) y= 1/cosx
show that dy/dx = secx tanx
Thanx.
Ive just got theses two problems:
help wud be much appreciated:
1) e^2x + e^2y = xy
Find dy/dx.
2) y= 1/cosx
show that dy/dx = secx tanx
Thanx.
0
Ralfskini
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#3
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#3
(Original post by Vahe10)
Ive just got theses two problems:
help wud be much appreciated:
1) e^2x + e^2y = xy
Find dy/dx.
2) y= 1/cosx
show that dy/dx = secx tanx
Thanx.
Ive just got theses two problems:
help wud be much appreciated:
1) e^2x + e^2y = xy
Find dy/dx.
2) y= 1/cosx
show that dy/dx = secx tanx
Thanx.
dy/dx = (y - 2e^2x)/(2e^2y - x)
2) dy/dx =-1cos^(-2)x * sinx = sinx/cos^2x = sinx/cosx* 1/cosx = secxtanx.
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Nylex
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#4
(Original post by Vahe10)
Ive just got theses two problems:
help wud be much appreciated:
1) e^2x + e^2y = xy
Find dy/dx.
2) y= 1/cosx
show that dy/dx = secx tanx
Thanx.
Ive just got theses two problems:
help wud be much appreciated:
1) e^2x + e^2y = xy
Find dy/dx.
2) y= 1/cosx
show that dy/dx = secx tanx
Thanx.
d/dx: 2e^2x + 2e^2y . dy/dx = y + xdy/dx
=> 2e^2y . dy/dx - xdy/dx = y - 2e^2x
=> dy/dx(2e^2y - x) = y - 2e^2x
=> dy/dx = (y - 2e^2x)/(2e^2y - x)
2. Quotient rule
d/dx (u/v) = (vdu/dx - udv/dx)/v^2
=> d/dx (1/cos x) = (cos x . 0 - 1 . -sin x)/cos^2 x
= sin x/cos^2 x
= (sinx/cos x) . 1/cos x
sin x/cos x = tan x, 1/cos x = sec x
=> d/dx = sec xtan x
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Ralfskini
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#5
(Original post by Nylex)
1. Implicit differentiation
d/dx: 2e^2x + 2e^2y . dy/dx = y + xdy/dx
=> 2e^2y . dy/dx - xdy/dx = y - 2e^2x
=> dy/dx(2e^2y - x) = y - 2e^2x
=> dy/dx = (y - 2e^2x)/(2e^2y - x)
1. Implicit differentiation
d/dx: 2e^2x + 2e^2y . dy/dx = y + xdy/dx
=> 2e^2y . dy/dx - xdy/dx = y - 2e^2x
=> dy/dx(2e^2y - x) = y - 2e^2x
=> dy/dx = (y - 2e^2x)/(2e^2y - x)
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Nylex
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elpaw
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#7
(Original post by Vahe10)
Ive just got theses two problems:
help wud be much appreciated:
1) e^2x + e^2y = xy
Find dy/dx.
2) y= 1/cosx
show that dy/dx = secx tanx
Thanx.
Ive just got theses two problems:
help wud be much appreciated:
1) e^2x + e^2y = xy
Find dy/dx.
2) y= 1/cosx
show that dy/dx = secx tanx
Thanx.
dy/dx (2e^2y - x) = y - 2e^2x
dy/dx = (y - 2 e^2x)/(2 e^2y -x)
2) y = sec x
dy/dx = secx tanx
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:P:P:P:P:P
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#8
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#8
(Original post by Ralfskini)
same as me but with more work.
same as me but with more work.
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