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Consider three simple functions F(x)=2x, G(x)=2x-6, H(x)=2x + π/2. We can differentiate these functions with respect to x to get F’(x)=f(x)=2, G’(x)=g(x)=2, H’(x)=h(x)=2. Clearly the derivatives of these fun...

Let A by any 2 by 2 matrix and the top left, top right, bottom left and bottom right entries be a, b, c and d respectively. The determinant for matrix A would be ad-bc.

1.)x 2 + y 2 = 10 2.)x + 2y = 5. Rearrange 2nd equation: x = 5 - 2y. Substitute back into 1st equation: (5 - 2y) 2 + y 2 = 10. Multiply out brackets: 4y 2 - 20y + 25 + y 2 = 10. Rearrange equation: 5y 2 - 20...

If we let y = lnx, we then know that x = e y . By differentiating both sides of this equation with respect to y we get:dx/dy = e y , as the exponential function differentiates to itself when differentiated w...

Take out all common factors, in this case only x. This leaves you with x(1-4x^2).Within the brackets you now have a quadratic equation which you can factorise. You need to find factors of -4x^2 that plus to ...