Exercise 1: Partial Derivatives of 3x^2y - y^3 — Possible Solution
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GIVEN
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f(x,y) = 3x^2*y - y^3

STEP 1: df/dx (TREATING y AS A CONSTANT)
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The term 3x^2*y: y is a constant multiplier, so applying the power
rule to x^2 gives d/dx[3x^2*y] = 3*y*2x = 6xy
The term -y^3: contains no x at all, so its derivative with respect
to x is 0.

df/dx = 6xy

STEP 2: df/dy (TREATING x AS A CONSTANT)
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The term 3x^2*y: 3x^2 is a constant multiplier, so
d/dy[3x^2*y] = 3x^2
The term -y^3: power rule gives d/dy[-y^3] = -3y^2

df/dy = 3x^2 - 3y^2

STEP 3: EVALUATE BOTH AT (1,2)
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df/dx at (1,2) = 6*1*2 = 12
df/dy at (1,2) = 3*1^2 - 3*2^2 = 3 - 12 = -9

RESULT
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df/dx(1,2) = 12
df/dy(1,2) = -9

Both match numerical differentiation results (12.0 and -9.0,
within expected floating-point precision).

WHY THIS WORKS AS AN ANSWER
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Each partial derivative is computed term by term, correctly
treating the other variable as a constant multiplier throughout
(per this chapter's own definition), and both final values are
independently confirmed against numerical differentiation.