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DOUBLE POINTS
Find the derivative.

DOUBLE POINTS Find the derivative.-example-1
User Joesdiner
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1 Answer

1 vote

Answer:


4√(16x^2+1)

Explanation:

Given
(d)/(dx) \int\limits^(4x)_ {1} \, √(t^2+1)\ dt

Using Fundamental Theorem of Calculus


(d)/(dx) \int\limits^(x)_ {a} \, f(t)dt =f(x)\ \ \ for\ any\ constant\ a


(d)/(dx) \int\limits^(4x)_ {1} \, √(t^2+1)\ dt=(d(4x))/(dx)(d)/(dx)\int\limits^(4x)}_(1)\, √(t^2+1)dt

Now,
(d(4x))/(dx)=4\ and\ (d)/(d(4x)) \int\limits^(4x)_ {1} \, √(t^2+1)\ dt=√((4x^2)+1)

Hence plugging these results we get:


(d)/(dx) \int\limits^(4x)_ {1} \, √(t^2+1)\ dt=4√((4x)^2+1)\\\\=4√(16x^2+1)

User Ramkee
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