math_proof 3 years ago find partial derivative Hx and Hy of H(x,y)=(y^2+1)e^x

1. cruffo

can you explain how you find the partial derivative with respect to x? Short sentance...

2. math_proof

you basically do derivative just with respect to x and treating y as a constant

3. zepdrix

So Mproof, Hmm If you take partials, you'll be treating the OTHER variable as a constant, meaning you won't have the product rule as it might seem at first glance. Does that help? :O

4. math_proof

like 3x^2y+2 fx=6xy and Fy is 3x^2

5. cruffo

6. math_proof

would Hx be 0?

7. cruffo

no. What is the regular derivative of f(x) = e^x?

8. math_proof

same

9. zepdrix

Think of the equation as Ce^x when taking the partial WRT x. Maybe that will help :)

10. math_proof

but don't you have to take a derivative of the (y^2+1) with respect to x?

11. zepdrix

no, thats just a constant attached to e^x :d

12. zepdrix

Maybe one thing you can do to convince yourself is, distribute the e^x to each term in the brackets. Then think about what you have :o

13. math_proof

so the derivative with respect to x will be the same as the given problem

14. zepdrix

ya :) good

15. math_proof

ooo I get it

16. math_proof

with respect to Y would it be 2ye^x?

17. zepdrix

(y^2 + 1)e^x = y^2 e^x + e^x Hy = 2y e^x + 0 Yes, very good ^^