What is the gradient of the quadratic function y=3x²?
The gradient of a function with variable x is found by applying the differential operator to it. The differential operator is commonly written as d/dx. Hence the differential operator applied to the function y is written to be dy/dx. The differential operator, in the generic polynomial case takes the function that it’s ‘operating’ on and takes a power of a polynomial inside the function, multiplies the entire function by the value of the power, then the polynomials power is decreased by one. I.e. If y=xn, for n being a real value. Then dy/dx=nxn-1. For the equation given, If y=3x2 then by the differential operator, dy/dx=(3)(2)x2-1=6x = gradient of y for all x being a real value.
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