Question #4492c

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Answer 1 · 2018-01-07T11:38:27

A) #d/dx (e^xsinx) = e^x (cosx +sinx ) #

B) #d/dx ( (x-1)/(x+1)) = 2/(x+1)^2#

C) #d/dx (1/(1-x^2)) = (2x)/(1-x^2)^2#

A) Using the product rule:

#d/dx (e^xsinx) = e^x d/dx sinx +sinx d/dx e^x#

#d/dx (e^xsinx) = e^x cosx +e^xsinx #

#d/dx (e^xsinx) = e^x (cosx +sinx ) #

B) Using the quotient rule:

#d/dx ( (x-1)/(x+1)) = ( (x+1)d/dx(x-1) - (x-1) d/dx (x+1))/(x+1)^2#

#d/dx ( (x-1)/(x+1)) = ( x+1 - x+1)/(x+1)^2#

#d/dx ( (x-1)/(x+1)) = 2/(x+1)^2#

C) Using the chain rule:

#d/dx (1/(1-x^2)) = -1/(1-x^2)^2 d/dx (1-x^2)#

#d/dx (1/(1-x^2)) = (2x)/(1-x^2)^2 = 2xy^2#