The graphs of f and g are shown. Let h(x) = f(g(x)) and s(x) = g(J(x)).Find each derivative , if it exists. If the derivative ve does not exist, explain why.Find h'( 1).

Question

The graphs of f and g are shown. Let h(x) = f(g(x)) and s(x) = g(J(x)).Find each derivative , if it exists. If the derivative ve does not exist, explain why.Find h&#039;( 1).

Willow Avery · Accepted Answer

To find the derivative of the function we will use Chain Rule:ddx[f(g(x))=f′(g(x))=g′(x)]h&#039;(x)=f&#039;(g(x))g&#039;(x)Plug in x=1 to find h&#039;(1).h&#039;(1)=f&#039;(g(1))g&#039;(1)=f&#039;(4)g&#039;(1)=(−1)⋅(−12)=12To estimate f&#039;(4), there is a part of the picture where we can see that the tangent line goes down 1 unit as the variable x moves one unit to the right. This means that it has slope -1, thus f&#039;(4)=-1.To estimate g&#039;(1), there is a part of the picture where we can see that the tangent line goes down 1 unit as the variable x moves two units to the right. This means that it hasslope −12, thus g′(1)=−12.Result:a=12

The graphs of f and g are shown. Let h(x) = f(g(x)) and s(x) = g(J(x)). Find each derivative , if it exists. If the derivative ve does not exist, explain why. Find h'( 1).

Open question

Answer & Explanation

New Questions in Calculus 1