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A table of values for $f, g, f' ,$ and $g'$ is given.(a) If $h(x) = f(g(x)),$ find $h'(1).$(b) If $H(x) = g(g(x)),$ find $H(1).$

a. 30b. 36

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Catherine R.

Missouri State University

Anna Marie V.

Campbell University

Kayleah T.

Harvey Mudd College

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Video Transcript

for party This problem we want to find aged prime of one and we know that h of x is f of G of X. So let's use the chain rule to find h prime at X h. Prime of X will be the derivative of the outside f prime of Jew vex times the derivative of the inside G prime of X. Now let's substitute one in their h prime of one will be f prime of G of one times g prime of one. Now we can refer to the table g of one is to and g prime of one is six so we can substitute those numbers in so h prime of one is f prime of to times six. Now we need to find f prime of to looking at the table f prime of two is five so we have five times six So the answer is 30 And for part B, we're finding h prime of one for capital H and capital H is g of f of X. So the derivative of capital age according to the chain rule will be the derivative of the outside G prime of f of X times a derivative of the inside F prime of X. So now let's evaluate that at one h prime of one will be G prime of F one times f prime of one. Now let's use the table to find f of one and effort one is three and f prime of one f prime of one is for. So let's substitute those numbers in and we have aged. Prime of one equals G prime of three times four. Now let's find you a prime of three. J Prime of three is nine. So let's substitute that in and we have nine times for so our answer is 36.

Oregon State University

Catherine R.

Missouri State University

Anna Marie V.

Campbell University

Kayleah T.

Harvey Mudd College

Lectures

Join Bootcamp