Below you can find the full step by step solution for you problem. We hope it will be very helpful for you and it will help you to understand the solving process.
(3*cos(0.5*x)-(0.5*x))'The calculation above is a derivative of the function f (x)
(3*cos(0.5*x))'+(-(0.5*x))'
(3)'*cos(0.5*x)+3*(cos(0.5*x))'+(-(0.5*x))'
0*cos(0.5*x)+3*(cos(0.5*x))'+(-(0.5*x))'
0*cos(0.5*x)+3*-sin(0.5*x)*(0.5*x)'+(-(0.5*x))'
0*cos(0.5*x)+3*-sin(0.5*x)*((0.5)'*x+0.5*(x)')+(-(0.5*x))'
0*cos(0.5*x)+3*-sin(0.5*x)*(0*x+0.5*(x)')+(-(0.5*x))'
0*cos(0.5*x)+3*-sin(0.5*x)*(0*x+0.5*1)+(-(0.5*x))'
0*cos(0.5*x)+3*0.5*(-sin(0.5*x))+(-(0.5*x))'
0*cos(0.5*x)+3*-0.5*sin(0.5*x)+(-(0.5*x))'
0.5*(x)'-1.5*sin(0.5*x)+(0.5)'*x
0.5*(x)'-1.5*sin(0.5*x)+0*x
0*x-1.5*sin(0.5*x)+0.5*1
-1.5*sin(0.5*x)-0.5
| Derivative of (sin(x)*cos(2*x)) | | Derivative of e^-x/1000 | | Derivative of -(5e^(-800x)) | | Derivative of 5e^(-200x) | | Derivative of 1/sin(2x^2) | | Derivative of 63/x | | Derivative of 10*10*10*10*10 | | Derivative of 7*22/7/4 | | Derivative of (1-e^6x)^3 | | Derivative of (3/5)*sin(8x) | | Derivative of (9/20)*cos(8x) | | Derivative of e^(-2x)*cos(6x) | | Derivative of e^(-2x)*sin(6x) | | Derivative of 1/(x*x^1/2) | | Derivative of 215.5Q | | Derivative of (3x^3-12) | | Derivative of 3t^3-12 | | Derivative of tan(8x^2) | | Derivative of 0.8(1-e^-2) | | Derivative of 50e^(x/100) | | Derivative of -e^(-0.2y) | | Derivative of (-4)*e^(6x)*sin(4x) | | Derivative of 6*e^(6x)*cos(4x) | | Derivative of 3(cos(3t)) | | Derivative of (e^(6x))*cos(4x) | | Derivative of 5x^2e^-3x | | Derivative of ln(e^4x) | | Derivative of x^2*e^(8x) | | Derivative of (X^3)-cos(x) | | Derivative of ln(90/x) | | Derivative of 7pi^5 | | Derivative of 8ln(5x^2) |