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Find the derivative...?

+3 votes
y= ∫ cos√(t) dt; from x^4 to 0

 

 

find dy/dx
asked Feb 8, 2013 in CALCULUS by andrew Scholar

2 Answers

+4 votes

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Derivative of an Integral (Fundamental Theorem of Calculus):

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Herer f(t) = cos√t so, f(x) = sin√x = y

y = sin√x

Apply derivatve each side.

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Derivative of Trigonometric Functions:

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image                             [ inner derivation of √x is 1/(2√x) ]

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answered Feb 9, 2013 by britally Apprentice

The derivative of y= ∫ cos√(t) dt; from x^4 to 0 is

image

0 votes

THE SECOND FUNDAMENTAL THEOREM OF CALCULUS : If f is continuous on an open interval I containing a, then, for every x in the interval, 

The integration function is .

Apply derivative each side with respect to x.

Let , and apply the Second Fundamental Theorem of Calculus with the Chain Rule as shown.

Apply Chain Rule :

Substitute .

Apply the Second Fundamental Theorem of Calculus :

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answered Jul 5, 2014 by casacop Expert

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