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1. Re-write f(x) as f(x) = 5x^(-1) - 9x + 42) Find first derivative as usual - multiply each term by it's power and subtract 1 from the power:f'(x) = (-1)(5x^(-2)) - (1)(9)Simplify to get f'(x) = -5/x^...

SInce, for y = uv, dy/dx = uv' + vu', where u' = du/dx, therefore:dy/dx = (1sin(x)) + (xcos(x)) = sin(x) + xcos(x)

We want to get the the sqrt(27) and sqrt(192) so that they have the same number in the square so they can then be added together. We will look at the factorisation of 27, 192. We can see 27 is divisible b...

as ln x is not a standard integral given in the formula booklet, but it’s derivative is a standard derivative, you can split ln x into 1 times ln x. This allows you to use the integral product rule method...

X=0,-5,1