- #1
Juwane
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To understand differentials better, I'm trying to use differentials dy and dx in the equation of the tangent line to the curve x^2 at point 3.
Here is the equation of the tangent line to the curve x^2 at point 3:
[tex]y=f'(3)(x-3)+f(3)=2(3)(x-3)+9=6(x-3)+9[/tex]
But since we are dealing with the tangent, why can't we write the above equation as:
[tex]y=\frac{dy}{dx}(x-3)+dy[/tex]
Since [tex]\frac{dy}{dx}=6[/tex] from which [tex]dy=6dx[/tex], we can rewrite the above as:
[tex]6(x-3)+6dx=6(x-3)+6(3)=6(x-3)+18[/tex]
Why this equation and the first equation aren't the same?
How else can the equation of tangent line be written in terms of dys and dxs?
Here is the equation of the tangent line to the curve x^2 at point 3:
[tex]y=f'(3)(x-3)+f(3)=2(3)(x-3)+9=6(x-3)+9[/tex]
But since we are dealing with the tangent, why can't we write the above equation as:
[tex]y=\frac{dy}{dx}(x-3)+dy[/tex]
Since [tex]\frac{dy}{dx}=6[/tex] from which [tex]dy=6dx[/tex], we can rewrite the above as:
[tex]6(x-3)+6dx=6(x-3)+6(3)=6(x-3)+18[/tex]
Why this equation and the first equation aren't the same?
How else can the equation of tangent line be written in terms of dys and dxs?
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