     suivant: Integration monter: Derivative and partial derivative précédent: Derivative and first order   Table des matières   Index

### Derivative and n-th order partial derivative : diff derive deriver

derive (or diff) may take more than two arguments : an expression and the names of the derivation variables (each variable may be followed by $n to indicate the number n of derivations). diff returns the partial derivative of the expression with respect to the variables given after the first argument. The notation$ is usefull if you want to derive k times with respect to the same variable, instead of entering k times the same variable name, one enters the variable name followed by $k, for example x$3 instead of (x,x,x). Each variable may be followed by a $, for example diff(exp(x*y),x$3,y$2,z) is the same as diff(exp(x*y),x,x,x,y,y,z) Examples • Compute : Input : diff(x*y ^2*z^3+x*y*z,x,z) Output : y^2*3*z^2+y • Compute : Input : diff(x*y ^2*z^3+x*y*z,x,z,z) Or input : diff(x*y ^2*z^3+x*y*z,x,z$2)
Output :
y^2*3*2*z
• Compute the third derivative of : Input :
normal(diff((1)/(x^2+2),x,x,x))
Or :
normal(diff((1)/(x^2+2),x\$3))
Output :
(-24*x^3+48*x)/(x^8+8*x^6+24*x^4+32*x^2+16)
Remark
• Note the difference between diff(f,x,y) and diff(f,[x,y]) :
diff(f, x, y) returns and
diff(f,[x, y]) returns [ , ]
• Never define a derivative function with f1(x):=diff(f(x),x). Indeed, x would mean two different things Xcas is unable to deal with: the variable name to define the f1 function and the differentiation variable. The right way to define a derivative is either with function_diff or:
f1:=unapply(diff(f(x),x),x)     suivant: Integration monter: Derivative and partial derivative précédent: Derivative and first order   Table des matières   Index
giac documentation written by Renée De Graeve and Bernard Parisse