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1. First the power will be taken into account: multiply by 10 and take one away from the power:
   y = 10(3x-1)^9
   2) Then we will differentiate what is in the brackets and multiply it by step 1:...

In this case the question has given you a clue as to the order that you solve the question. So, first we need to expand the brackets, multiplying each term by one another to get; y=8x^6 - 36x^4 + 6x^3 - 2...

Firstly, we need to differentiate the function of the curve y = x^3 + 2x^2 - 5. Using d/dx (x^n) = nx^(n - 1), we get dy/dx = 3x^2 + 4x. To find the gradient of this curve, we then need to evaluate dy/dx ...

You have a general quadratic of the form: ax^2 + bx + c = 0, where a,b,c are constants (although is consistent for functions). Divide by a (assuming a/=0, this would not be a quadratic in that case):x^2 +...

We know that x²+kx-3k-5<0 for some x for the values the k that we are trying to find.This will only occur when the curve has two distinct intersections with the x-axis. There are two distinct intersect...