Question

would the derivative of 2x-(x^2)(tanx) by using the chain rule be 2-(2x^3)(tanx)(sec^2)(x)?
and would the derivative of xcosx-sinx by using the chain rule be (-xsinx)-cosx?

Answer 1

\[y=2x-x^2\tan x\\
y'=2-\left(2x\tan x+x^2\sec^2x\right)\]
\[y=x\cos x-\sin x\\
y'=\left(\cos x-x\sin x\right)-\cos x=-x\sin x\]
No chain rule here; straight up product rule.