If y=5x+4x^3, find dy/dx.

When asked to find dy/dx, this means to differentiate. Differentiation is also a method of calculating the gradient of a line. (dy/dx = gradient.) The rule of differentiation is as follows: Step 1: Differentiate each term individually. Step 2: Multiply the coefficient by the power. Step 3: Then subtract one from the power. Following Step 1, we will take 5x and 4x^3 separately. Following Step 2, we will take the 5x term and multiply the coefficient by the power which in this case is 15=5. Following Step 3 we will subtract one from the power giving us 0 meaning the differential of this term is 5 as x^0 is equal to 1. We will then do the same for the 4x^3 term. Following Step 2 we will have 34=12, followed by Step 3 of subtracting one from the power giving us 2. Differential of the second term is therefore 12x^2. Finally, the answer is equal to 5+12x^2.