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
You can use the product rule for this. But it is probably simpler to open the parentheses first, and then use the rule for the derivative of polynomials.
It is 2x - 10.
It is 2(x - 5).
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 )
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