Search over 10,000 free study notes

Use the chain rule: dy/dx = dy/du * du/dx
Let y = ln(2x^3+x+8)Let u = 2x^3+x+8
dy/dx = d/dx (ln(2x^3+x+8)) = dy/du * du/dx
dy/du = 1/udu/dx = 6x^2 + 1
dy/dx = 1/u * (6x^2 + 1) = (1/(2x...

Pythagoras’ theorem is the formula used to calculate any side of a right-angled triangle. The concept is that the square of the hypotenuse is equal to the sum of the squares on the other two sides. Assign...

So to integrate this function we would need to use a method called Integration by parts that you may have come across in your studies.
This is where we separate the function into two parts to make it...

This is a inequality question. There are two separate inequalities and the values n can take are the solutions of n that overlap between the 2 inequalities. First inequality: 3n< 12 therefore n <4 ....

If 6x + 2y = 26 then 26 - 6x = 2yy = 13 - 3xSo, using the substitution method.... into 8x + 3y = 328x + 3(13 - 3x) = 328x + 39 - 9x = 32-x + 39 = 3232 + x = 39x = 39 - 32 = 7Sub x = 7 into 6x + 2y = 266(7...