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)=9e7x f'(x)=63e7x, g(x)=12e2x g'(x)=24e2x
y'(x)=(63e7x.12e2x-24e2x.9e7x)/(12e2x)2
y'(x)=(756e9x-216e9x)/144e4x=540e9x/144e4x=15e5x/4
At x=2/5, y'(x)=15e2/4=27.709
CM
