Differentiating Complex Functions with Respect to x

[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?

 

[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.

 

[Air]

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

That makes more sense.

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.

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

 

[neutrino]

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

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

 

[Air]

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

Ok. I understand. Thanks for the help.