Suppose that f2 5 g2 2 f 2 3 and g2 4 find a if hx 5fx 4gx...

Suppose that f(2) = ?5, g(2) = 2, f '(2) = ?3, and g'(2) = 4. find (a) if h(x) = 5f(x) ? 4g(x) h'(2) = (b) if h(x) = f(x)g(x) h'(2) = (c) if h(x) = f(x)/g(x) h'(2) = (d) if h(x) = g(x)/1 + f(x) h'(2) =

Transcript

00:01 In this problem, suppose that f2 equals to minus 5, f dash 2 is equal to f dash 2 is equal to minus 3 here, and g2 is equal to 2 and g dash 2 is equal to 4.

00:19 So these are the given conditions to us, right? and it is telling that if a function is given to us for every part, in every part, that for a part a suppose, it is given that if h x is equals to 5 f of x right so it is that asked that what is h dash 2 so we will just differentiate this equation and we will put x equals to 2 this is what we are going to do here this is so simple is that so h dash 2 will be equal to 5 f dash x yes so this equation is here now we will put x equals to 2 then we will get h2 equals to 2 equals to 5 f -2 so we know these values already given right so 5 f -dash -2 that means 5 into minus 3 that will give us minus 15 all right so now for the second part we have h x is equals to f x g x right so then h -dash -x will be what so on differentiation it is a product rule that h -dash x is equals to f -dash -x g x plus f x g dash x all right so when x equals to 2 then h dash 2 equals to f dash 2 g 2 plus f 2 g 2 right so all that values we know already given so when we will put this we will get minus 6 minus 20 that is minus 26 so h dash 2 here is minus 26 now for the part see we can see here if h x is equal to f x by g x so we can say that here h dash 2 is what so here this is the division rule right for the differentiation so after differentiation we will get f dash x g x x minus f x d dash x divided by g x whole square right so now we will get we will put all the values that is my you can say f dash 2 g2 this is when x equals to 2 right so this will be minus f2 g dash 2 right this is divided by g2 whole square right so when we will solve this we will get 14 by 4 as an answer so what will be simplified form let us see so the simplified form will be 7 by 2.

03:06 So 7 by 2 is answer or almost you can say 3 .5 is the answer.

03:13 Right.

03:13 So both are correct.

03:15 I hope this helps.

03:17 So now for the part last and the fourth part we can see if hx is equal to gx by 1 plus fx right.

03:28 So, h -dash -x is given by g -dash -x, right? so this will be g -dash -x into, in brackets, it will be 1 plus f -x, right? so when we will just subtract it, we will get f -dash -x upon 1 plus fx whole square, right? isn't that so easy? yes.

03:52 So now when we will solve it, we will get, we will just write here x equals to so when x is equal to 2 then h dash 2 will be equal to g dash 2 1 plus f 2 right minus f dash 2 into g 2 right so this is divided by 1 plus f2 whole square right so what are those values let us see so g dash 2 is equal is 4.

04:31 Isn't that same thing? okay, yes...

Question

Suppose that f(2) = ?5, g(2) = 2, f '(2) = ?3, and g'(2) = 4. find (a) if h(x) = 5f(x) ? 4g(x) h'(2) = (b) if h(x) = f(x)g(x) h'(2) = (c) if h(x) = f(x)/g(x) h'(2) = (d) if h(x) = g(x)/1 + f(x) h'(2) =

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