# Math Help - Differentiation question ... need help!!!

1. ## Differentiation question ... need help!!!

A curve has the equation y=root x(k-x) where k is a constant.
Given that the gradient of the curve is root 2 at the Point P where x=2.

a. find the value of k.

b.show that the normal to the curve at P has the equation
x+root 2y=c where c is an integer to be found.

i got the solutions k = 2.5/2.0625
is the right???

3. I got $k\;=\;12+4\sqrt{6}$
How did you get your value ?

4. You made a mistake in the differentiation of y
$(u^n)'\;=\;nu'u^{n-1}$

You forgot u'

5. what's u'???
i thought the first derivative is defined as:
dy/dx = n(x^(n-1))

6. The first derivative of y=x^n is y'=n x^(n-1)

But the first derivative of y=(u(x))^n is y'=n u'(x) (u(x))^(n-1)

Here u(x)=kx-x² and n=1/2