I. Evaluate: for:
Note: diff(f) return and diff(f,2) returns
syms x
f = 1/x
f = 
diff(f)
ans = 
diff(f,x,2)
ans = 
f = exp(x) + ( 3 / sqrt(x)) + tan(x)
f = 
diff(f)
ans = 
diff(f,2)
ans = 
f = x^(3/2) + 5 * cos(x)
f = 
diff(f)
ans = 
diff(f,2)
ans = 
f = exp(x ^ 2 - 2 * x)
f = 
diff(f)
ans = 
diff(f,2)
ans = 
f = log(x^2)
f = 
diff(f)
ans = 
diff(f,2)
ans = 
f = tan(5 * x ^ 7 + 3 * x ^ 4)
f = 
diff(f)
ans = 
diff(f,2)
ans = 
f = sinh(x^2 + 3*x)
f = 
diff(f)
ans = 
diff(f,2)
ans = 
f = log(cos(x))
f = 
diff(f)
ans = 
diff(f,2)
ans = 
syms t w
f = exp(-x*t) * cos(w*t)
f = 
diff(f)
ans = 
diff(f,2)
ans = 
f = (1 - exp(-x/5))/5
f = 
diff(f)
ans = 
diff(f,2)
ans = 
f = 1/2*(log(cosh(sqrt(t))))
f = 
diff(f)
ans = 
diff(f,2)
ans = 
f = cos(x)/(1+sin(x))
f = 
diff(f)
ans = 
diff(f,2)
ans = 
f = 5*t*(exp(-5*t))
f = 
diff(f)
ans = 
diff(f,2)
ans = 
II. Evaluate: for:
Note: Commands are given in sequence to find
clear
clc
syms t
x = (t - 3)^2
x = 
y = t^3 - 1
y = 
dy = diff(y)
dy = 
dx = diff(x)
dx = 
dydx = dy/dx
dydx = 
d2ydx2 = diff(dydx,t)
d2ydx2 = 
x = sin(t)
x = 
y = cos(t)
y = 
dy = diff(y)
dy = 
dx = diff(x)
dx = 
dydx = dy/dx
dydx = 
d2ydx2 = diff(dydx,t)
d2ydx2 = 
x = exp(t-1)
x = 
y = exp(t/2)
y = 
dy = diff(y)
dy = 
dx = diff(x)
dx = 
dydx = dy/dx
dydx = 
d2ydx2 = diff(dydx,t)
d2ydx2 = 
syms r theta
x = r *(theta - sin(theta))
x = 
y = r*(1-cos(theta))
y = 
dy = diff(y)
dy = 
dx = diff(x)
dx = 
dydx = dy/dx
dydx = 
d2ydx2 = diff(dydx,theta)
d2ydx2 = 
clear
syms x y
f = x^3 + y^3 - 2*x - 3
f = 
dfdx = diff(f,x)
dfdx = 
% dfdy = diff(f,y)
d2fdx2 = diff(f,x,2)
d2fdx2 = 
%d2fdy2 = diff(f,y,2)
syms a
a = 2
a = 2
f = log(x-a) - log(x^2) - log(y)
f = 
dfdx = diff(f,x)
dfdx = 
% dfdy = diff(f,y)
d2fdx2 = diff(f,x,2)
d2fdx2 = 
% d2fdy2 = diff(f,y,2)
f=exp(x+y) + sin(x)
f = 
dfdx = diff(f,x)
dfdx = 
% dfdy = diff(f,y)
d2fdx2 = diff(f,x,2)
d2fdx2 = 
% d2fdy2 = diff(f,y,2)
y = x^sin(x)
y = 
diff(y,x)
ans = 
diff(y,x,2)
ans = 
y = exp(x * (x^2 +1))/sin(x)
y = 
diff(y,x)
ans = 
diff(y,x,2)
ans = 
f = log(exp(1) +y) - exp(sin(x+y))
f = 
dfdx = diff(f,x)
dfdx = 
% dfdy = diff(f,y)
d2fdx2 = diff(f,x,2)
d2fdx2 = 
%d2fdy2 = diff(f,y,2)
III. Partial Difference Find for:
NOTE:
clear
clc
syms x y
f = x^2+2*x*y+y^2
f = 
diff(f,x)
ans = 
diff(f,y)
ans = 
diff(f,x,2)
ans = 
diff(f,y,2)
ans = 
diff(f,y,x)
ans = 
f = x^3+y^2*cos(x)
f = 
diff(f,x)
ans = 
diff(f,y)
ans = 
diff(f,x,2)
ans = 
diff(f,y,2)
ans = 
diff(f,y,x)
ans =