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In order to solve this problem we will have to use the product rule as follows: d/dx[x^3⋅cos(5⋅x)]=[d/dx(x^3)]⋅cos(5x)+(x^3)⋅[d/dx[cos(5x)]]=(3⋅x^2)⋅cos(5⋅x)+(x^3)⋅−5⋅sin(5⋅x)=3⋅x^2⋅cos(5⋅x)−5⋅x...

a) For finding the midpoint M, the point M must be equidistant from P and Q in both the x and y axes. Hence, we consider the x and y axis separately. The midpoint of the x coordinates is essentially a mea...

We are told f(x) = (2x-5)^2 (x+3).In part b) we are asked to show that f'(x) = 12x^2 -16x -35, so for part (c) we shall assume this definition for f'(x). We are told that the x coordinate for A is 3. Call...

The aim of the question is to equate x= into an expression.Step 1. Look to see if you can simplify the equation. On the left hand side of the equation you can see that 3 is a factor of 12. And also a fact...