The Curve C has equation y = 3x^4 - 8x^3 - 3. Find dy/dx.
The question is asking us to differentiate the equation y = 3x^4 - 8x^3 - 3. To differentiate this equation, we must differentiate term-by-term. In order to differentiate a term, we must multiply the coefficient of the x-term by the power that the x-term is raised to and then reduce the power by one.
So lets begin by differentiating the term 3x^4. We multiply the coefficient (3) by the power that the x is raised to (4) and then reduce the power of the x by 1. Thus when we differentiate 3x^4, we get 12x^3. Similarly, lets differentiate the next term, -8x^3. We multiply the coefficient (-8) by the power of x (3) and then reduce the power of x by one. Hence, differentiating -8x^3 gives us -24x^2. The last term (-3) is a constant. When we differentiate constants, we always get zero as there is no x-term present. So differentiating -3 gives us 0. By grouping each differentiated term, the answer to our question is dy/dx = 12x^3 -24x^2.
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