amyna one year ago find the derivative: y=(x^2+csc(-5x))^3/2 thank you!

1. amyna

|dw:1437845982011:dw|

2. IrishBoy123

$$y=(x^2+cosec(-5x))^{3/2}$$ that it? suggest you share what you have done/ what the problem is

3. anonymous

$2x^{1}-2/15\csc(-5x)^{-1/3}$

4. amyna

i used chain rule and got 3/2(x^2+csc(-5x))^1/2 (2x-csc(-5x)cot(-5x)*5 ? i don't know if thats right?

5. Loser66

right but + instead of - at the last term. |dw:1437846650378:dw|

6. IrishBoy123

is this what you are saying? $$(3/2)(x^2+csc(-5x))^{1/2} (2x-csc(-5x)cot(-5x).5)$$

7. amyna

yes

8. IrishBoy123

look at @Loser66 's sketch $$(cosec \ x)^\prime = - cosec \ x \ cot \ x$$

9. IrishBoy123

sorry, @loser66 was trying to make this point: $$d/dx (-5x) = -5$$. so you have: $$\frac{3}{2}(x^2+cosec(−5x))^{1/2} \ \ (2x−cosec(−5x)cot(−5x)(-5))$$ $$\ = \frac{3}{2}(x^2+cosec(−5x))^{1/2} \ \ (2x+5 \ cosec(−5x)cot(−5x))$$ next, i'd be really tempted to clean out those $$-5x$$'s within the trig functions but maybe you are happy

10. amyna

thanks! it makes more sense now!