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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^...

x = 4.5y = -1.5To answer this question, first, rearrange the first equation to make y the subject: 5x + y = 21 --> y = 21 - 5xYou can now substitute this value of y into the second equation: x - 3(21 -...

∫sin(2x + 1)dx[newline]In this case the easiest way to solve the integral is to perform a substitution. The substitution should reduce the integral to something you can solve. In this case we will[newline...

Via inspection, one can factorise this via the difference of squares; since a^2-b^2 = (a+b)(a-b), therefore:100-x^2 = (10-x)(10+x)

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