(a) the function k is defined by k(x)=f(x)g(x). find k′(0).

(b) the function m is defined by m(x)=f(x)/2g(x). find m′(5).

(c) find the value of x for −1

(a) k'(0) = f'(0)g(0) + f(0)g'(0)

(b) m'(5) =

Step-by-step explanation:

(a) Since k(x) is a function of two functions f(x) and g(x) [ k(x)=f(x)g(x) ], so for differentiating k(x) we need to use product rule,i.e.,

this will give k'(x)=f'(x)g(x) + f(x)g'(x)

on substituting the value x=0, we will get the value of k'(0)

{for expressing the value in terms of numbers first we need to know the value of f(0), g(0), f'(0) and g'(0) in terms of numbers}{If f(0)=0 and g(0)=0, and f'(0) and g'(0) exists then k'(0)=0}

(b) m(x) is a function of two functions f(x) and g(x) [ ]. Since m(x) has a function g(x) in the denominator so we need to use division rule to differentiate m(x). Division rule is as follows :

this will give

on substituting the value x=5, we will get the value of m'(5).

{for expressing the value in terms of numbers first we need to know the value of f(5), g(5), f'(5) and g'(5) in terms of numbers}

{NOTE : in m(x), g(x) ≠ 0 for all x in domain to make m(x) defined and even m'(x) }

{ NOTE : }

the answer is 62

step-by-step explanation: