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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 ...

Notice that y can be expressed as y=f(x)g(x), in which f(x)=e^(2x) and g(x)=x^2-4x-2.Through the product rule, we know that dy/dx=f'(x)g(x)+f(x)g'(x).Through the chain rule, we can solve f(x) by rewriting...