Chain Rule - Partial Derivatives - dw/dt Express dw/dt as function of **t** , if **w = xy** , **x = cos t** , **y = sen t** , **z = t** My first step is to sketch the tree. _w - x - t_ _w - y - t_ _w - z - t_ * * * dw/dx = y dw/dy = x dw/dz = 1 Then: dx/dt = -sen t dy/dt = cos t dz/dt = 1 Then: -ysent + xcost + 1 Changing the x and y to "cos t and sen t" Result: * **-sen²t + cos²t + 1** But the teacher's answer is: **1 + cos2t** What's is incorrect?

Nothing. They used the identity

$$ \cos 2x = \cos^2 x - \sin^2 x $$

to obtain what was written.