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A curve is defined by the parametric equations; x=(t-1)^3, y=3t-8/(t^2), t~=0. Find dy/dx in terms of t.

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
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Answered by Nadia C. • Maths tutor
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Solve the following equation: x^(3) - 6x^(2) + 11x - 6 = 0

x 3 - 6x 2 + 11x - 6 = 0 Let (x-a)(x-b)(x-c) = x 3 - 6x 2 + 11x - 6=> abc = -6 and a + b + c = -6 From abc=-6, find the possibilities of their values: (1,2,-3), (1,-2,3), (-1,2,3), (-1,-2,-3), (1,1,-6), (...
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Answered by Ellie-May H. • Maths tutor
8367 Views

How would I differentiate y = 3xy + 2x^2 + x^2y^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 ys. ...
EO
Answered by Emelia O. • Maths tutor
17107 Views

How do I calculate the eigenvalues and eigenvectors of a 2x2 matrix, and what is the point of doing this calculation?

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 a d - b c, we set this equal to zero and solve ...
TD
Answered by Tutor120184 D. • Maths tutor
5594 Views

Find the derivative of y=e^(2x)*(x^2-4x-2).

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 in...
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Answered by Samuel H. • Maths tutor
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