# Differentiation math homework

1. May 12, 2007

### Air

Differentiate with respect to x

dy = 3x^2 - 5√x + 1/2x^2
dx

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I don't understand how to differentiate this part: 5√x + 1/2x^2. I think changing it to indices form would be: x^1/5 + (2x)^-2?

How can it be worked out?

2. May 12, 2007

### neutrino

$$5\sqrt{x}$$ is not $$(x)^{\frac{1}{5}}$$. It is five times $$(x)^{\frac{1}{2}}$$.

The last term is a bit ambiguous, the way you've typed it. Is it $$\frac{1}{2}x^2$$ or $$\frac{1}{2x^2}$$? Anyway, neither cannot be simplified to (2x)^-2.

3. May 12, 2007

### Air

That makes more sense.

It's $$\frac{1}{2x^2}$$

4. May 12, 2007

### neutrino

It's then (1/2)(x^-2). (2x)^-2 would be (1/4)(x^-2).

5. May 12, 2007

### Air

Ok. I understand. Thanks for the help.