Example 2: find the derivative of (3χ²+4x)⁴

Solution: we simply use chain Rule because the function is defined in terms of powers.
Chain Rule formula :
dy/dx= dy/du × du/dx
To use chain Rule formula is pretty simple, you just let the functions in the bracket be u.
So let u=3χ²+4x so that du/dx=6x+4
Now let y= u² so that dy/du=2u
Now that we've obtained all the necessary derivatives in the chain Rule formula. We can now go ahead with substitution into the formula.
dy/dx = dy/du × du/dx
dy/dx= 2u(6x+4) but u=3χ²+4x so

dy/dx=2( 3χ²+4x)(6x+4) and hence the answer... If you like you can expand the answer..