By using the chain rule: dy/dx = dy/du x du/dx
With y = tan2x
Let u = tan x
Then:
y = u2
du/dx = d/dx tan x = sec2x
dy/dx = dy/du x du/dx
= 2u sec2x
= 2 tan x sec2x
Chat with our AI personalities
sin x times sin x. or 1/cosec2(x) or 1 - cos2(x) or tan2(x)*cos2(x) etc, etc.
y = Sin(x) dy/dx = Cos(x)
You should apply the chain rule d/dx(x.sin x) = x * d/dx(sin x) + sin x * d/dx(x) = x * cos x + sin x * 1 = x.cos x + sin x
The chain rule states that the derivative of f(g(x)) is f'(g(x))⋅g'(x). In other words, it helps us differentiate *composite functions*. For example, sin(x²) is a composite function because it can be constructed as f(g(x)) for f(x)=sin(x) and g(x)=x².
f(x) = Cos(x) f'(x) = -Sin(x) Conversely f(x) = Sin(x) f'(x) = Cos(x) NB Note the change of signs.