Thread: rate of change dy/dx

Find the rate of change (dy/dx) for the prescribed value of x.

y = (x^2 + 2) (x + square root of x) x=4
y = (x^2 + 2)(x + x^-1/2)
y = (x^2 + 2)(1/2square root x) + (x + 1/2square root of x)(2x)

If that is correct thus far, how do I go about multipling this out?

Originally Posted by becky

Find the rate of change (dy/dx) for the prescribed value of x.
y = (x^2 + 2) (x + square root of x) x=4
y = (x^2 + 2)(x + x^-1/2)
y = (x^2 + 2)(1/2square root x) + (x + 1/2square root of x)(2x)
If that is correct thus far, how do I go about multipling this out?

Hello,

you've got:



Obviously you don't know the product rule to calculate the derivative of y. So you have to multiply first:



Now differentiate:



Plug in the value you know and you'll get:

=



Greetings

EB