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How do you differentiate # -(2/(3x)) #?

Answer 1

Cameron Alexander

See below for two solutions.

If you want to use the quotient rule , you can.

#d/dx(-2/(3x)) = -d/dx(2/(3x))#

# = -[((0)3x-2(3))/(3x)^2]#

# = -[(-6)/(9x^2)] = 6/(9x^2) = 2/(3x^2)#

Alternatively , you can rewrite the expression before differentiating.

#d/dx(-2/(3x)) = d/dx(-2/3x^-1)#

Now use the power and constant multiple rules.

# = (-1)(-2/3)x^(-1-1) = 2/3x^-2 = 2/(3x^2)#

Use whichever method you like.

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Answer 2

Aurora Alvarado

To differentiate -(2/(3x)), you can use the power rule and the chain rule for differentiation. The derivative of -(2/(3x)) with respect to x is:

d/dx [-(2/(3x))] = -d/dx [(2/(3x))] = -[d/dx (2/(3x))] = -[-2/(3x^2)] = 2/(3x^2)

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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.