Quote:
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Originally Posted by arcticdragon
function derivative
sin cos
cos -sin
tan sec^2
cot -csc^2
sec sec * tan
csc -csc * cot
anyone see the patern?
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The "co" functions are all negative. Also, Maple is for sissies, MatLab is a real man's tool.
A derivative is the rate of change of the function. Or more precisely, if f' is the derivative of f, and f is differentiable at a (more on that some other time) f'(a) is the slope of the tangent line of the function where x = a.
Also, Yan, I don't think you need logarithmic differentiation to solve this (you are thinking of integrals maybe?) only implicit differentiation
proof:
to find dy/dx of the function y=atan(x)
first move the tan to the other side
tan(y) = x
take the derivitive of both sides
sec^2(y) * dy/dx = dx/dy
devide over sec^2(y) so that
dy/dx = 1/sec^2(y) * dx/dy
remember trig?
since sec^2(y) = 1 + tan^2(y)
dy/dx = 1/(1 + tan^2(y)) * dx/dy
and tan(y) = x (from the top)
dy/dx = 1/(1 + x^2) * dx/dy
math is fun
-Andy