# Math Help - differentiation

1. ## differentiation

p41 q40
$y = (x^2 ) \sqrt {1-x}$
show that $\frac {dy}{dx} = \frac {2y}x - \frac {x^4} { 2y}$

i can only get
dy / dx = 1/2 $x(1-x)^{-1/2} (4-5x)$

2. Hello,

Originally Posted by afeasfaerw23231233
p41 q40
$y = (x^2 ) \sqrt {1-x}$
show that $\frac {dy}{dx} = \frac {2y}x - \frac {x^4} { 2y}$

i can only get
dy / dx = 1/2 $x(1-x)^{-1/2} (4-5x)$
I don't really understand what you wrote...

Nevermind.

$y^2=x^4 (1-x)$

Differentiating :

$2 \cdot \frac{dy}{dx} \cdot y=-x^4+4x^3(1-x)$

$2 \cdot \frac{dy}{dx} \cdot y=-x^4+4x^3-4x^4$

$2 \cdot \frac{dy}{dx} \cdot y=-x^4+4(x^3-x^4)$

$2 \cdot \frac{dy}{dx} \cdot y=-x^4+4\cdot \underbrace{(1-x)}_{y^2} \cdot x^3$

Divide both sides by $2 \cdot y$