Derivative of e^(-(1/3)x^2-(1/5)y^4) ?

[engstudent363]

Derivative of e^(-(1/3)x^2-(1/5)y^4) ?

I need help figuring this out. I know that the derivative of e^5x is 5e^x but I'm not sure what to do when x is raised to a power or when there is another variable involved, such as y. Once again here is what I need to find: Derivative of e^(-(1/3)x^2-(1/5)y^4)

And if you guys know of a way that I can display that in a clearer way such as with some type of symbol tool please let me know for future posts. To make that clearer I want to find the derivative of e raised to the power of (negative one-third x^2 minus one-fifth y^4). Also, if you know of a site that fully explains the derivatives of e and includes explanations to the above problem let me know. Thanks.

 

[b_schoenfeld]

It may just be a typo on your part, but the derivative of e^5x is 5e^5x, not 5e^x.

With derivatives of e^(stuff), you start out by simply re-writing e^(stuff) and then multiplying by the derivative of (stuff). Like in e^5x, you re-write e^5x and then multiply by the derivative of 5x, which is five, giving you 5e^5x.

In your problem, you re-write your original term and then multiply by the derivative of
(-(1/3)x^2-(1/5)y^4) which is (-(2/3)x-[((4/5)y^3)dy/dx]) using implicit differentiation. The final answer would then be {-(2/3)x-[((4/5)y^3)dy/dx]}e^(-(1/3)x^2-(1/5)y^4).