Could someone help me work out the first derivative

[rfk]

This one has me stumped
I need to find the first derivative of the following formula:

0.8 * ((100-0.05x)^λ-1/λ) + 0.2 * ((100+0.2x)^λ-1/λ)

I don't even know where to start. If some one could show me a worked example I would be eternally grateful.

I can do it for the parts in brackets but what do I do with the multiplication constant.

Using the power rule I get:



λ(100-0.05x)^λ-1 for the first part
λ(100+0.2x)^λ-1 for the second part

I know the derivative of both parts is additive so that f'(x) = lhs'(x) + rhs'(x) but as I said what do I do with the 0.8 and 0.2?

Thanks

Rob

[Math Tutor]

f(x) = 0.8 * ((100-0.05x)^λ-1/λ) + 0.2 * ((100+0.2x)^λ-1/λ)

f'(x) = g'(x) + h'(x)
where g(x) = 0.8 * ((100-0.05x)^λ-1/λ)
and h(x) = 0.2 * ((100+0.2x)^λ-1/λ)

g(x) = 0.8 * (100-0.05x)^λ- 0.8*(-1/λ)
g'(x) = 0.8 *λ (100-0.05x)^{λ - 1}.(100-0.05x)' =
0.8 *λ*(100-0.05x)^{λ - 1}*(0-0.05)

[Math Tutor]

What about the first derivative of h(x) - h'(x) ?

[Blackcap]

I don't even know where to start. If some one could show me a worked example I would be eternally grateful....???




_________
watson