Question

please differentiate given problem. ​

Answer 1

Answer:

dy/dx = 2x

Step-by-step explanation:

First notice that

$\displaystyle e^{a\log x}=\left(e^{\log x}\right)^a=x^a$

So the given function can be simplified first:

$\displaystyle y=\frac{e^{5\log x} - e^{4\log x}}{e^{3\log x} - e^{2\log x}}\\\\{}\ \ =\frac{x^5-x^4}{x^3-x^2}\\\\{}\ \ =\frac{x^4(x-1)}{x^2(x-1)}\\\\{}\ \ =x^2$

Now it is easy to see that

$\displaystyle\frac{dy}{dx} = 2x$