1. ## derivative.. problem

hello

I need some help with finding the derivative of 4x(squareroot 1-x^2)

Please look at the drawing, the correct answer is in green ,I cant seem to get it?
Thanks

2. Hi wolfhound,

just use a combination of the product rule and chain rule to solve.

$\displaystyle \frac{d}{dx}4x\sqrt{1-x^2}=4x\frac{d}{dx}\sqrt{1-x^2}+\sqrt{1-x^2}\frac{d}{dx}4x$

$\displaystyle =(4x)0.5(1-x^2)^{-0.5}(-2x)+\sqrt{1-x^2}(4)$

$\displaystyle =\frac{-4x^2}{\sqrt{1-x^2}}+\frac{4(1-x^2)}{\sqrt{1-x^2}}$

since $\displaystyle \frac{\sqrt{1-x^2}\sqrt{1-x^2}}{\sqrt{1-x^2}}=\frac{1-x^2}{\sqrt{1-x^2}}$

3. Originally Posted by wolfhound
hello

I need some help with finding the derivative of 4x(squareroot 1-x^2)

Please look at the drawing, the correct answer is in green ,I cant seem to get it?
Thanks
$\displaystyle y=4x\sqrt{1-x^2}$

$\displaystyle y'=4\sqrt{1-x^2}+4x(\frac{1}{2}(1-x^2)^{-\frac{1}{2}}\cdot -2x)$

4. Thanks , But I still cannot finish the question to find the answer in the green,
how do I do this?

5. The final two fractions now have a common denominator, wolfhound.
They can now be added to get the result in green.

See my earlier post and how the denominators are made equal.