mat 21c (iii) quiz 7

df/dt

df/dx * dx/dt + df/dy * dy/dt

implicit differentiation dy/dx =

- Fx/Fy

write lim

for each step

derivative of cosx=

-sinx

derivative of cos2x=

-2sin2x

cos²x + sin²x=

1

derivative of ln(1+4t)=

4/(1+4t)

dz/dx partial derivative

y is constant

implicit differenetiation; dz/dx =

-Fx/Fz

$$\nabla f=$$

$$\left\langle\frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z}\right\rangle$$

D_uf =

$\nabla f$ . u

u =

u / |u|

cos²t + sin²t =

1

Tangent Plane Equation

Fx(x-x0) + Fy(y-y0) + Fz(z-z0) = 0

Normal line parametric equation:

x = x0 + (Fx)t ; y = y0 + (Fy)t ; z = zo + (Fz)t

normal n =

(Fx, Fy, Fz)