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Let’s solve this step by step.

We are given a set of functions and asked to find their derivatives using the power rule.

The power rule says:
> If f(x) = xⁿ, then f’(x) = n·x^(n−1)

Also, if there’s a constant multiplier (like 5 in 5x³), we keep it and multiply it by the derivative of xⁿ.

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Let’s go one by one:

1. f(x) = x²
→ Derivative: 2·x^(2−1) = 2x¹ = 2x ✔

2. g(x) = x³
→ Derivative: 3·x^(3−1) = 3x² → but wait! The answer shown is “3/x²” — that’s wrong.
Actually, 3x² is correct. But let me check again — maybe it's written differently?
No — 3/x² would be 3x^(-2), which is not the derivative of x³.
So the image has an error here. Correct derivative is 3x²

Wait — looking back at the image, it shows for g(x)=x³ → answer is "3/x²" — that must be a typo or misprint. We’ll compute correctly.

But hold on — perhaps I misread? Let me double-check all.

Actually, looking carefully at the original image text:

It says:
- f(x) = x² → 2x ✔️
- g(x) = x³ → 3/x² ✘ (should be 3x²)
- h(x) = 1/x → -1/x² ✔️ (since 1/x = x⁻¹ → derivative is -1·x⁻² = -1/x²)
- k(x) = √x → 1/(2√x) ✔️ (√x = x^(1/2) → derivative = (1/2)x^(-1/2) = 1/(2√x))
- m(x) = 2x⁵ → 10x⁴ ✔️ (2×5=10, x⁵→x⁴)
- n(x) = 5x³ → 15x² ✔️ (5×3=15, x³→x²)
- p(x) = 6x⁴ → 24x³ ✔️ (6×4=24, x⁴→x³)
- q(x) = 7x⁶ → 42x⁵ ✔️ (7×6=42, x⁶→x⁵)

So only g(x) = x³ has an incorrect answer listed as “3/x²” — it should be 3x²

But since the problem asks us to solve based on what’s shown, and assuming the student wants the correct math, we’ll provide accurate answers.

However — wait! Maybe the image meant something else? Let me re-read the user input.

User said: “You are an educational assistant helping a student solve homework problems.” And provided an image with tasks.

In the image, for g(x)=x³, the answer written is “3/x²” — which is clearly wrong. Probably a handwriting or printing error.

As an educator, I should correct it.

So final correct derivatives:

1. f(x) = x² → 2x
2. g(x) = x³ → 3x²
3. h(x) = 1/x → -1/x²
4. k(x) = √x → 1/(2√x)
5. m(x) = 2x⁵ → 10x⁴
6. n(x) = 5x³ → 15x²
7. p(x) = 6x⁴ → 24x³
8. q(x) = 7x⁶ → 42x⁵

All others match except #2.

Since the instruction is to solve accurately, I will list the correct ones.

Final Answer:
2x, 3x², -1/x², 1/(2√x), 10x⁴, 15x², 24x³, 42x⁵