Find the derivative:
y=2e^(x^2+1)^3
i have so far 2(2x)e^(x^2+1)^3
Is this correct? How do I simplify furthere if it is?
Hmmmm.
d/dx (f(x))= d/du(f(u)) du/dx
let u= (x^2+1)^3
y= 2e^u
dy/du= 2e^u
du/dx= 3*(x^2+1)^2 * 2x
so...
dy/dx= dy/du *( du/dx)
Yes, you've made some progress! To simplify it further, you just need to substitute the expressions you found for dy/du and du/dx back into the equation.
you found:
dy/du = 2e^u
du/dx = 6x(x^2 + 1)^2
So, substituting these values back into the equation:
dy/dx = (2e^u) * (6x(x^2 + 1)^2)
Now we need to substitute back the value of u:
u = (x^2 + 1)^3
Substituting u = (x^2 + 1)^3 into the equation:
dy/dx = (2e^((x^2 + 1)^3)) * (6x(x^2 + 1)^2)
This is the simplified expression for the derivative dy/dx.