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If y = sin(cos(tan(x)))
Using the chain rule: (f(g(x)))' = f'(g(x)).g'(x)
Then dy/dx = cos(cos(tan(x))).-sin(tan(x)).sec2(x)
= -cos(cos(tan(x))).sin(tan(x)).sec2(x)
Unfortunately I don't think this can be simplified much more.
( sec = 1/cos )
Assuming y = x(x - 10) Either use the product rule: u = x v = (x - 10) → y = x(x - 10) = uv d/dx (uv) = v du/dx + u dv/dx → dy/dx = d/dx x(x - 10) = (x - 10)(d/dx x) + (x)(d/dx (x - 10)) = (x - 10)(1) + (x)(1) = x - 10 + x = 2x - 10 or expand the brackets and differentiate dy/dx = d/dx x(x - 10) = d/dx x² - 10x = 2x - 10