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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 ad - bc, we set this equal to zero ...

Answered by Tutor120184 D. • Maths tutor

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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...

Answered by Samuel H. • Maths tutor

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Find the derivative of y = 3x^4 - 10x^2+7x

The method used to find the derivative (dy/dx) of the equation is to:

"Multiply the coefficient of x by the power then deduct the power x is raised to by 1"

Step 1: 3x^4

Answered by Hameedat O. • Maths tutor

3009 Views

How do i use chain rule to calculate the derivative dy/dx of a curve given by 2 "parametric equations": x=(t-1)^3, y=3t-8/t^2

(Explain why it is called "parametric"). The definition of chain rule says that we can re-write the derivative dy/dx in terms of the "parameter t" by dy/dx = (dy/dt) X (dt/dx). (Expla...

Answered by Adil F. • Maths tutor

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Find the first three terms of the binomial expansion of (3 + 6x)^(1/2).

To find the binomial expansion of this expression we need to use a formula. The formula states that for expressions of (1 + x)ⁿ it can be written as: 1 + nx + (n(n-1)x²)/2 ...
A...

Answered by Brendan W. • Maths tutor

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