week 15 discussion

\[f(x,y)=x^3−3x+y^2−6y\ at\ (−1,3)\]

#6.

f1 <- expression(x**3 - 3*x + y**2 - 6*y) 
x <- -1
y <- 3

fx1 <- D(f1, "x")
fx1

## 3 * x^2 - 3

fy1 <- D(f1, "y")
fy1

## 2 * y - 6

eval(fx1)

## [1] 0

eval(fy1)

## [1] 0

\[f(x,y)=ln(xy)\ at \ (−2,−3)\]

#8.

f2<- expression(log(x*y)) 
x <- -2
y <- -3

fx2 <- D(f2, "x")
fx2

## y/(x * y)

fy2 <- D(f2, "y")
fy2

## x/(x * y)

eval(fx2)

## [1] -0.5

eval(fy2)

## [1] -0.3333333