Question

Derivative of:

(x)(sqroot: 4-x)

Answer 1

\(\dfrac d{dx}x\sqrt{4-x}\) am I correct

Answer 2

Use product rule and then chain rule :)

Answer 3

Yes, you're correct. When I found the derivative I got 4-3x over (2)(sqroot: 4-x) but the answer says that in the numerator 4 should be an 8..

Answer 4

\[\frac d{dx}x\sqrt{4-x}\]\[=1\cdot\sqrt{4-x}+x\cdot\frac{-1}{2\sqrt{4-x}}\]\[=\frac{2(4-x)}{2\sqrt{4-x}}-\frac x{2\sqrt{4-x}}\]

Answer 5

I hope that explains the \(8\) :)

Answer 6

In the first step, where did the -1 come from in the numerator?

Answer 7

chain rule, \(\dfrac d{dx}(4-x)=-1\) :)

Answer 8

Okay I see it - Thank you so much!

Answer 9

no problem :)