Diferentiating

$$\\y=(5+x^2)^{3/2}\\\\
y'=\frac{3}{2}(5+x^2)^{1/2}\times (0+ 2x)\\\\
y'=\frac{3}{\not{2}}(5+x^2)^{1/2}\times \not{2}x\\\\
y'=3x(5+x^2)^{1/2}\\\\$$

So yes your answer is correct.

Do you have any questions?

If the function is:  f(x) = 3/2,  then  f'(x) = 0.

It is important to remember that the first derivative gives the gradient of the tangent.

now you have the line y=3/2

This line is parallel to the x axis so the gradient is 0

I.e.  The first derivative is 0

Huh? Actually don't you take 1 from it?

I'm having to differentiate (5+x^2)^3/2 and i got 3x(5+x^2)^1/2. Is that not right?

thanks

Thankyou, that's great!