Question

How do you differentiate `f(x)=e^(x^2)/(e^x-x^2)` using the quotient rule?

Answer 1

`\frac{(e^{x^2}*2x)(e^x-x^2)-e^{x^2}(e^x-2x)}{(e^x-x^2)^2}`

Explanation:

Quotient rule:

`d/dx f(x)/g(x) = \frac{f'g-fg'}{g^2}`

Let's compute all the functions we need:

• `f(x) = e^{x^2}`
• `f'(x) = e^{x^2}*2x`
• `g(x) = e^x-x^2`
• `g'(x) = e^x-2x`
• `g^2(x) = (e^x-x^2)^2`

Let's plug these values into the formula:

#\frac{f'g-fg'}{g^2} = \frac{(e^{x^2}*2x)(e^x-x^2)-e^{x^2}(e^x-2x)}{(e^x-x^2)^2}#