#C++14, (削除) 165 (削除ここまで)(削除) 138 (削除ここまで)(削除) 133 (削除ここまで)(削除) 112 (削除ここまで) 110 bytes

Generic Variadic Lambda saves a lot. -2 bytes for #import and deleting the space before <

#import<cmath>
#define A auto
A f(A x){return 0;}A f(A x,A a,A b,A...p){return a*b*std::pow(x,b-1)+f(x,p...);}

Ungolfed:

#include <cmath>
auto f(auto x){return 0;}
auto f(auto x,auto a,auto b,auto...p){
 return a*b*std::pow(x,b-1)+f(x,p...);
}

Usage:

int main() {
 std::cout << f(19,4,3,-2,4,5,10) << std::endl;
 std::cout << f(400,0,4) << std::endl;
 std::cout << f(-13,4,0,5,1) << std::endl;
 std::cout << f(-3,4.14,4,48,2) << std::endl;
 std::cout << f(5.4,1,3,-5,0) << std::endl;
}

C++14, (削除) 165 (削除ここまで)(削除) 138 (削除ここまで)(削除) 133 (削除ここまで)(削除) 112 (削除ここまで) 110 bytes

Generic Variadic Lambda saves a lot. -2 bytes for #import and deleting the space before <

#import<cmath>
#define A auto
A f(A x){return 0;}A f(A x,A a,A b,A...p){return a*b*std::pow(x,b-1)+f(x,p...);}

Ungolfed:

#include <cmath>
auto f(auto x){return 0;}
auto f(auto x,auto a,auto b,auto...p){
 return a*b*std::pow(x,b-1)+f(x,p...);
}

Usage:

int main() {
 std::cout << f(19,4,3,-2,4,5,10) << std::endl;
 std::cout << f(400,0,4) << std::endl;
 std::cout << f(-13,4,0,5,1) << std::endl;
 std::cout << f(-3,4.14,4,48,2) << std::endl;
 std::cout << f(5.4,1,3,-5,0) << std::endl;
}

#C++14, (削除) 165 (削除ここまで) (削除) 138 (削除ここまで) (削除) 133 (削除ここまで) (削除) 112 (削除ここまで) bytes

Generic Variadic Lambda saves a lot. -2 bytes for #import and deleting the space before <

#import<cmath>
#define A auto
A f(A x){return 0;}A f(A x,A a,A b,A...p){return a*b*std::pow(x,b-1)+f(x,p...);}

Ungolfed:

#include <cmath>
auto f(auto x){return 0;}
auto f(auto x,auto a,auto b,auto...p){
 return a*b*std::pow(x,b-1)+f(x,p...);
}

Usage:

int main() {
 std::cout << f(19,4,3,-2,4,5,10) << std::endl;
 std::cout << f(400,0,4) << std::endl;
 std::cout << f(-13,4,0,5,1) << std::endl;
 std::cout << f(-3,4.14,4,48,2) << std::endl;
 std::cout << f(5.4,1,3,-5,0) << std::endl;
}

#C++14, (削除) 165 (削除ここまで) (削除) 138 (削除ここまで) (削除) 133 (削除ここまで) (削除) 112 (削除ここまで) 110 bytes

Generic Variadic Lambda saves a lot. -2 bytes for #import and deleting the space before <

#import<cmath>
#define A auto
A f(A x){return 0;}A f(A x,A a,A b,A...p){return a*b*std::pow(x,b-1)+f(x,p...);}

Ungolfed:

#include <cmath>
auto f(auto x){return 0;}
auto f(auto x,auto a,auto b,auto...p){
 return a*b*std::pow(x,b-1)+f(x,p...);
}

Usage:

int main() {
 std::cout << f(19,4,3,-2,4,5,10) << std::endl;
 std::cout << f(400,0,4) << std::endl;
 std::cout << f(-13,4,0,5,1) << std::endl;
 std::cout << f(-3,4.14,4,48,2) << std::endl;
 std::cout << f(5.4,1,3,-5,0) << std::endl;
}

#C++14, (削除) 165 (削除ここまで) (削除) 138 (削除ここまで) (削除) 133 (削除ここまで) 112 bytes

Generic Variadic Lambda saves a lot

#include <cmath>
#define A auto
A f(A x){return 0;}A f(A x,A a,A b,A...p){return a*b*std::pow(x,b-1)+f(x,p...);}

Ungolfed:

#include <cmath>
auto f(auto x){return 0;}
auto f(auto x,auto a,auto b,auto...p){
 return a*b*std::pow(x,b-1)+f(x,p...);
}

Usage:

int main() {
 std::cout << f(19,4,3,-2,4,5,10) << std::endl;
 std::cout << f(400,0,4) << std::endl;
 std::cout << f(-13,4,0,5,1) << std::endl;
 std::cout << f(-3,4.14,4,48,2) << std::endl;
 std::cout << f(5.4,1,3,-5,0) << std::endl;
}

#C++14, (削除) 165 (削除ここまで) (削除) 138 (削除ここまで) (削除) 133 (削除ここまで) (削除) 112 (削除ここまで) bytes

Generic Variadic Lambda saves a lot. -2 bytes for #import and deleting the space before <

#import<cmath>
#define A auto
A f(A x){return 0;}A f(A x,A a,A b,A...p){return a*b*std::pow(x,b-1)+f(x,p...);}

Ungolfed:

#include <cmath>
auto f(auto x){return 0;}
auto f(auto x,auto a,auto b,auto...p){
 return a*b*std::pow(x,b-1)+f(x,p...);
}

Usage:

int main() {
 std::cout << f(19,4,3,-2,4,5,10) << std::endl;
 std::cout << f(400,0,4) << std::endl;
 std::cout << f(-13,4,0,5,1) << std::endl;
 std::cout << f(-3,4.14,4,48,2) << std::endl;
 std::cout << f(5.4,1,3,-5,0) << std::endl;
}