Finding d/dx

Question

                4x

Find  d/dx ∫√t² +1dt

               ¹

√4x+1

√16x²+1+√2

4√16x²+1

√16x² + 1

 

Answer 1

4√16x²+1  assuming that the original integrand was √(t²+1). This parenthesization is necessary to explicitly indicate the scope of the radical symbol.

 

Reason: just substitute 4x for t in the original integrand, and use the chain rule factor 4 from differentiation of 4x, the upper limit of the definite integral.  The differentiation d/dx "knocks out" the ∫ ... dx parts (inverse operations), according to Fundamental Theorem of Calculus.