Find g'(x) for g(x)= e^(x)/(1+x^(2)) What rule do you use here?

Question

jhannybean · Answer

$$g(x) = \frac{e^x}{1+x^2}\implies e^x(1+x^2)^{-1}$$ Depends on how you want to solve it,eitehr product rule with what I transformed the function to, or quotient rule,

perl · Answer

you can use quotient rule

anonymous · Answer

ok so I got this for the product rule e^(x)*(1+x^(2))^(-1)+e^(x) and how do you find the derivative for (1+x^(2))^(-1)?

jhannybean · Answer

$$\frac{d}{dx} x^n = nx^{n-1}$$

jhannybean · Answer

$$f'(x) = f'g+g'f \implies e^x(1+x^2)^{-1} -1e^x(1+x^2)^{-2}(2x)$$

jhannybean · Answer

Write it so that you have all positive variables.$$f'(x)=\frac{e^x}{(1+x^2)^2}-\frac{2xe^x}{(1+x^2)^2}$$$$f'(x)=\frac{e^x(1-2x)}{(1+x^2)^2}$$

anonymous · Answer

ok I understand how you got that now. Thank you :)

jhannybean · Answer

No problemo :)