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How do you find the derivative of #y=1/x^7?

Answer 1

Scarlett Allison

#dy/dx=-7/x^8#

#"differentiate using the "color(blue)"power rule"#

#•color(white)(x)d/dx(ax^n)=nax^(n-1)#

#y=1/x^7=x^-7#

#rArrdy/dx=-7x^((-7-1))=-7x^(-8)=-7/x^8#

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Answer 2

Paisley Johnson

To find the derivative of ( y = \frac{1}{x^7} ), you can use the power rule for differentiation, which states that if ( y = ax^n ), then ( \frac{dy}{dx} = anx^{n-1} ). Applying this rule to the given function, we have:

[ \frac{dy}{dx} = -7x^{-8} ]

So, the derivative of ( y = \frac{1}{x^7} ) is ( \frac{dy}{dx} = -7x^{-8} ).

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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.