Quocient rule!
Let's just remember the quocient rule by definition, here:
be y=(f(x))/(g(x))y=f(x)g(x), then its derivative is given by:
y'=(f'(x)*g(x)-f(x)*g'(x))/(f(x)^2)y'=f'(x)⋅g(x)−f(x)⋅g'(x)f(x)2.
Now, let's just derivate your function accordingly:
(dy)/(dx) = (1.7t^(0.7)*(t^(1.4)+6)-(t^1.7+8)(1.4t^0.4))/(t^1.7+8)^2dydx=1.7t0.7⋅(t1.4+6)−(t1.7+8)(1.4t0.4)(t1.7+8)2
(dy)/(dx) = ((1.7t^2.1+10.2t^0.7)-1.4t^2.1+11.2t^0.4)/(t^1.7+8)^2dydx=(1.7t2.1+10.2t0.7)−1.4t2.1+11.2t0.4(t1.7+8)2
(dy)/(dx) = (0.3t^2.1+10.2t^0.7-11.2t^0.4)/(t^1.7+8)^2dydx=0.3t2.1+10.2t0.7−11.2t0.4(t1.7+8)2