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Home Q & A Board Science-Related Homework Help Mathematics
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tony12 tony12
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11 years ago
I need to know the full solution using the definition of derivative
and not the quotient rule or anything. Please give me a link!
Or you can just explain too.
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wrote...
#1
11 years ago
Have you even tried to solve it on your own ?
The definition of derivative is in your textbook and/or notes. Just replace with your function f(x)=tanx and find the limit.
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TontinTontin
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11 years ago
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#3
11 years ago
let y = tan(x) = sin(x)/cos(x)

let be the small change in x,  h causes a small change g in y, So

y + g = sin(x + h) / cos(x + h)

g = sin(x + h)/cos(x + h) - sin(x) /cos(x)

g = {sin(x + h)cos(x) - cos(x + h)sin(x)}/cos(x + h)cos(x)

but remember sin(x + h)cos(x) - cos(x + h)sin(x) = sin(x + h - x) = sin(h)

you may have known sin(A - B) = sin(A)cos(B) - cos(A)sin(B)

g = sin( x + h - x) /cos(x + h)cos(x) = sin(h)/cos(x + h)cos(x)

By definition

lim h Rightwards Arrow 0 value of (g/h) = dy/dx = sin(h) /h * 1/cos(x)cos(x)

but as h--> 0 sin(h)/h will be  equal to1,

therefore,  dy/dx = 1/cos^2(x) = sec^2x
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