Find the gradient of the exponential curve y(x)=(9e^(7x))/(12e^(2x)) at x=2/5

According to the quotient rule, when y(x)=f(x)/g(x), y'(x)=(f'(x)g(x)-g'(x)f(x))/g(x)²

f(x)=9e^7x f'(x)=63e^7x, g(x)=12e^2x g'(x)=24e^2x

y'(x)=(63e^7x.12e^2x-24e^2x.9e^7x)/(12e^2x)²

y'(x)=(756e^9x-216e^9x)/144e^4x=540e^9x/144e^4x=15e^5x/4

At x=2/5, y'(x)=15e²/4=27.709