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06032013  #1 
Join Date: Jun 2013
Posts: 1

(Calculus)Differentiation and its application
Hello! I was wondering if anyone could assist me on a few calculus questions, any help would be appreciated, thanks
Determine the differentials of the following functions and calculate the gradient at the given point: a) y= x22+ 1/x2 (x= 2) b) y= 2ex+3x2+2 (x= 0) c) y= sin2x + tanx (x= 45̊) 
06052013  #2  
Join Date: Dec 2008
Posts: 249

Quote:
a. y = x^2  2 + (1/x^2) (x = 2) y = x^2  2 + x ^(2) dy/dx = 2x  2x^(3) dy/dx (at x = 2) = 2(2)  2((2)^(3)) = 4  (1/4) = 3 3/4 = 15/4 b. y = 2e^x + 3x^2 + 2 (x = 0) dy/dx = 2e^x + 6x dy/dx (at x = 0) = 2(e^0) + 6(0) = 2 + 0 = 2 c. y = sin(2x) + tan(x) (x = 45 degs.) dy/dx = 2cos(2x) + (sec(x))^2 dy/dx (at x = 45) = 2cos(90) + (sec(45)(sec(45)) = 0 + 2 = 2 I hope that is how you meant your notation for the different functions. 

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