# f(a,b) y a,b f(a,b) y a,b

## Full text

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### a,b

= change in output f as x changes, with y fixed

= change in output f as y changes, with x fixed

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x=x0

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### y z

2D Input space 1D Output space

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### dy

Tangent vector = (dx,dy) = (1, dy/dx)= (1, f’(a))

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### ) with normal vector (a,b,c)?

Arbitrary point (x,y,z) on plane

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### y z

2D Input space 1D Output space

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(4)

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### lying in the slicing plane

Tangent vector with slope

### So one tangent vector is

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### ) z

Tangent vector with slope

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### tangent plane

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### (No—I can’t draw it!)

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### y(t) y

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### They are the same! And the new way is much easier in complicated cases

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## -1 Find

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### Step 5: Take the limit as ∆t goes to zero:

This is not much of a proof—but gives the idea of why the terms are added

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x

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### t find

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## References

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