Search over 10,000 free study notes

This is an example of a question where you would use the product rule, where if y = uv then dy/dx = udv/dx + vdu/dx. In this case u = 2x and v = ln(x). So first of all we will differentiate 2x wh...

dy/dx=(dy/dt)*(dt/dx); dy/dt=3+16t^-3; dx/dt=3(t-1)²; dt/dx=1/3(t-1)²; dy/dx=(3+16t^-3)/3(t-1)²

x³ - 6x² + 11x - 6 = 0
Let (x-a)(x-b)(x-c) = x³ - 6x² + 11x - 6=> abc = -6 and a + b + c = -6 From abc=-6, find the possibilities of their values: (1,2,...

Since this problem contains both xs and ys on the right hand side, we need to use implicit differentiation. This is where we use the chain rule to differentiate with regards to x the terms which contain y...

We find the eigenvalues (here called "k") by solving the characteristic equation det(M - kI) = 0. For a 2x2 matrix ((a, b), (c,d)) the determinant is ad - bc, we set this equal to zero ...