Using implicit differentiation, write the expression "3y^2 = 4x^3 + x" in terms of "dy/dx"
To differentiate this expression with respect to "x", any terms comprising of an "x" must multiply their powers with their numerical values and subtract 1 from the power. However to differentiate a non-"x" term with respect to "x" we need to do it differently. The value of the "y" term must be multiplied by "dy/dx" before it can be differentiated as normal. The process looks like this:
3y2 -> 3y2 (dy/dx) -> 6y(dy/dx). Therefore the differential is 6y(dy/dx) = 12x2 + 1. However, the question asks for the answer in terms of "dy/dx", so we must manipulate the expression by dividing both sides by "6y". Then we get the final answer of:dy/dx = (12x2 + 1)/6y.
