Question

Find the second and third derivatives of the following functions by using Matlab

1. f(x) = 3cosx-2sinx x² 2. f(x) = ln(x) - 1 3. f(x) = 5x3 - 2x2 + 7x + 10

Answer 1

eig.mx mdof.mx partCQ2.mx 1 4 clc syms x f = (3* cos(x)-2*sin(x))/(x^2); % second derivative d2 = diff(f,2) % third derivative d3 = diff(f,3) 5 6 7 - COMMAND WINDOW d2 = (4*(2* cos(x) + 3* sin(x)))/x^3 - (3* cos(x) - 2*sin(x))/x^2 + (6*(3* cos(x) - 2* sin(x)))/x^4 d3 = (2*cos(x) + 3* sin(x))/x^2 + (6*(3* cos(x) - 2*sin(x)))/x^3 - (18*(2*cos(x) + 3* sin(x)))/x^4 - (24*(3* cos(x) - 2* sin(x)))/x^5

+ eig.mx mdot.mx partCQ2.mx - 3 1 4 1 clc 2 syms x f = log(x)-1; % second derivative d2 = diff(f,2) % third derivative 7 - d3 = diff(f,3) 8 COMMAND WINDOW 5 1 6 d2 = - 1/x^2 d3 = 2/x^3

1 clc 2 syms x 3 f = 5*x^3-2*x^2+7*x+10; 4 % second derivative 5 d2 = diff(f,2) % third derivative 7 d3 = diff(f,3) 8 COMMAND WINDOW 6 d2 = 30*x - 4 d3 = 30 >>

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