f(x_) = (x^15) + 4 (x^13) + 5 (x^7) + 3 x + 4; 
((∂f(x))/(∂x))

f(x_) = (3/((x^3) + 2 x + 5)); 
((∂f(x))/(∂x))

f(x_) = (((x^2) - 4)/((x^2) + 4)); 
((∂f(x))/(∂x))

f(x_) = (((x^2) + 3 x + 5)/((x^2) + 4)); 
((∂f(x))/(∂x))
Together[((∂f(x))/(∂x))]

f(
          x_) = (((x^3) - (1/((x^2) + 1)))/((x^4) + (1/((x^2) + 1)))); 
Simplify[((∂f(x))/(∂x))]

f(x_) = (1/(1 - ((2 x)/((x^2) + 1)))); 
Simplify[((∂f(x))/(∂x))]

f(x_) = sin(x) ((x^15) + 4 (x^13)); 
((∂f(x))/(∂x))

f(x_) = (sin^2)(x) ((x^15) + 4 (x^13)); 
((∂f(x))/(∂x))

f(x_) = ((tan(x))/((x^3) + 2 x + 5)); 
((∂f(x))/(∂x))
Simplify[Together[((∂f(x))/(∂x))]]

f(x_) = sin(x) cos(x); 
((∂f(x))/(∂x))

f(x_) = sin(x) (E^x); 
((∂f(x))/(∂x))

f(x_) = ((E^x)/(sin(x))); 
((∂f(x))/(∂x))

f(x_) = ((sin(x))/((x^2) + 4)); 
((∂f(x))/(∂x))
Together[((∂f(x))/(∂x))]

f(x_) = (((x^2) + 3 x + 5)/(cos(x))); 
((∂f(x))/(∂x))

f(x_) = ((((x^2) + 2) sec(x))/((x^5) - (x^3) + 1)); 
((∂f(x))/(∂x))
Simplify[Together[((∂f(x))/(∂x))]]