Question Solved1 Answer Suppose that functions f and g and their derivatives with respect to x have the values shown to the right at x = 2 and x3. Find the derivatives with respect to x of the combinations below at the given values of 96x) 2 2 7 1 7 3x 3 2 -1 5 a. 2f(x) x=2 b. f(x) + g(x), x= 3 c. f(x)=9(x) x=3 f(x) d. x=2 e. f(g(x)) = 2 1.V)x=2 g. hf(x)+9°(x), x=2 a. The derivative of 21(x) with respect to xatx2 is (Simplify your answer. Type an exact answer, using * as needed)
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GIVEN:xf(x)g(x)f '(x)g '(x)2721/7-532-13815A. DERIVATIVEOF 2f(x) = 2f '(x)So, 2 f '(2) =2*(1/7)=2/7 ,at x=2 { from table we see that f'(x)=1/7 at x=2}B.DERIVATIVE OF f(x)+g(x) =f '(x)+g '(x)=f '(3)+g '(3)=381+5{from table we see that f '(x)=381and g '(x)=5 at x=3}DEIVATIVE OF f (x)+g (x) = 381+5,at x=3C.DERIVATIVE OF f(x)*g(x) =f '(x)g(x)+g '(x)f(x)=f '(3)g(3)+g '(3)f(3)=()(-1)+(5)(2){from table we see that f '(x)=381,g(x)=-1 ,f(x)=2 and g '(x)=5  at x=3}DERIVATIVE OF f (x)*g (x)= -3pi+10 ,at x=3D. DERIVATIVEOF  f(x)//g(x)={ f '(x)g(x)-g '(x) f(x)} /g 2(x)= {f '(2)g(2)-g '(2)f(2) }/g 2(2)={(1/7)*2-(-5)*7}/(2)2 {from table we see thatf(2)=7,f '(2)=1/7,g(2)=-5 and g'(2)=-5}=247/28DERIVATIVE OF f (x)/g (x) = 247/28 ,at x=2   E. BY APPLYINGCHAIN RULEDERIVATIVE OF f(g(x)) = f '(g(x))*g '(x)=f '(g(2))*g '(2)=f '(2) *g '(2) { from table we see tha ... See the full answer