# Answer to Question #1703 in Calculus for Natalia

Question #1703

Suppose k '(1) = 2.

(a) If f(x) = k(5x), find f '(1/5).

(b) If g(x) = k(x+ 2), find g '(-1).

(c) If h(x) = k(x / 7), find h '(7).

(a) If f(x) = k(5x), find f '(1/5).

(b) If g(x) = k(x+ 2), find g '(-1).

(c) If h(x) = k(x / 7), find h '(7).

Expert's answer

(a) If f(x) = k(5x) then f'(x) = 5 k'(5x), f'(1/5) = 5 k'(5*1/5) = 5;

(b) If g(x) = k(x +2) then g'(x) = k'(x+2),& g'(x) = k'(-1 +2) = 1;

(c) If h(x) = k(x/7) then h'(x) = 1/7 k'(x/7), h'(x) = 1/7 k'(7/7) = 1/7.

(b) If g(x) = k(x +2) then g'(x) = k'(x+2),& g'(x) = k'(-1 +2) = 1;

(c) If h(x) = k(x/7) then h'(x) = 1/7 k'(x/7), h'(x) = 1/7 k'(7/7) = 1/7.

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