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We want to find dy/dx. We find this using the product rule by setting the functions f(x) = x and g(x) = e^2x. With these functions, we can write the equation as y = f(x)g(x), so by applying the ...

Set x^2-5x-14=0. So (x-7)(x+2)=0So function meets x-axis at (-2,0) and (7,0).
To find turning point, differentiate function and set equal to 0.2x-5=0. So x=5/2. Substitute x=5/2 into f(x) to give y c...

answer may not be obvious at first, but by using intergration by parts, treating part 1 as lnx and part 2 as 1, you will get xlnx-1

y=(4/3)x³-2x²-24x+16Step 1: Understand the questiondy/dx means differentiate the function of y with respect to xturning points are where the gradient of the function changes and will...

(a) To differentiate implicitly, differentiate x’s as normal and differentiate y’s with respect to y before multiplying by dy/dx. Therefore the differentiating the curve gives
9x^(1/2) + 10y*(dy/dx) ...