Question

How does this help me learn calculus?
Our derivative calculator shows every step of the solution process, explaining which rules were applied and why. This helps you understand the method, not just get the answer. Combine this with our video tutorials, practice problems, and worksheets for comprehensive calculus mastery.

Answer 1

How to Calculate
Simply differentiate with respect to the chosen variable, treating all other variables as constants!

💡 Example 1: Basic Partial Derivatives
Given: f(x, y) = x³y² + 2xy - 5y

Find ∂f/∂x: (Treat y as a constant)

∂/∂x[x³y²] = 3x²y² (Power rule, y² is constant)
∂/∂x[2xy] = 2y (y is constant)
∂/∂x[-5y] = 0 (−5y is constant with respect to x)
Answer: ∂f/∂x = 3x²y² + 2y
Find ∂f/∂y: (Treat x as a constant)

∂/∂y[x³y²] = 2x³y (x³ is constant)
∂/∂y[2xy] = 2x (x is constant)
∂/∂y[-5y] = -5
Answer: ∂f/∂y = 2x³y + 2x - 5

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Answer 2

wait huh..

Answer 3

that just hurt my brain more

Answer 4

how ?

Answer 5

Why do we assume
∥
h
p
∥
→
1
∥h
p

∥→1?
A: This normalization simplifies the problem without loss of generality. If
∥
h
p
∥
→
c
≠
0
∥h
p

∥→c

=0, we can rescale all vectors by
1
/
c
1/c. The general solution is
lim
⁡
⟨
b
p
,
z
p
⟩
=
0.9375
×
0.9
c
2
lim⟨b
p

,z
p

⟩=
c
2

0.9375×0.9

.

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Answer 6

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