# Thread: Derivate and differential equation

1. ## Derivate and differential equation (Mod: move to calculus)

Hello

1 Derivate the function $\frac{3}{\sqrt{x - 9} }$

2 General solution for $y' - 3y = e^{-2x} + 2$

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1 I think I have solved this:

First, lets see the expression as two factors:

$3 * (x - 9)^{-\frac{1}{2}}$

Derivate of an product $u' * v + u * v'$

Gives us:

$3* -\frac{1}{2}(x - 9)^{-\frac{3}{2}} + 0 * (x - 9)^{-\frac{1}{2}}$

$\frac{3}{2(x - 9)^{\frac{3}{2}}}$

2, I don't know, we haven't really studied differential equations that much.

Thanks for all replies

2. With constants, you don't need to use the product rule (it gives the correct answer still, though).

But, you forgot to transcribe your negative sign.

meaning:
$f(x) = 3 (x-9)^{-1/2}$

$f\prime (x) = 3*\frac{-1}{2}(x-9)^{-3/2}*1$

$f\prime (x) = -\frac{3}{2}(x-9)^{-3/2}$

no need for product rule, just chain rule, and since x-9 differentiates to 1, it doesn't even really matter if you use the chain rule on this one.