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How do you differentiate #y=5x^6-sec^-1x#?

Answer 1

#dy/dx=30x^5-1/(xsqrt(x^2-1)#

#y=5x^6-sec^-1x# #dy/dx=d/dx(5x^6-sec^-1x)# Using sum rule #=d/dx(5x^6)-d/dx(sec^-1x)# #d/dx(5x^6)=5.d/dx(x^6)# #=(5)(6)x^(6-1)=30x^5# #d/dx(sec^-1x)=1/(xsqrt(x^2-1)# Thus, #dy/dx=30x^5-1/(xsqrt(x^2-1)#

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Answer 2

Emily Ammerman

To differentiate ( y = 5x^6 - \sec^{-1}(x) ), you would differentiate each term separately. The derivative of ( 5x^6 ) is ( 30x^5 ), and the derivative of ( \sec^{-1}(x) ) is ( -\frac{1}{|x|\sqrt{x^2-1}} ). Therefore, the derivative of the given function is:

[ y' = 30x^5 + \frac{1}{|x|\sqrt{x^2-1}} ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.