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How do you find the derivative of #y=(x+8)^5#?

Answer 1

Luke Alvarez

#5(x+8)^4#

#u=x+8# #y=u^5#

Differentiate u and y

#u'=1# #y'=5u^4#

#u' * y' = 1 * 5u^4#

sub u back into the answer.

#5(x+8)^4#

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Answer 2

Charles Anctil

To find the derivative of ( y = (x + 8)^5 ), use the power rule for differentiation.

Rewrite the function as a power function. ( y = (x + 8)^5 )
Apply the power rule: ( \frac{d}{dx}(x^n) = nx^{n-1} ). ( \frac{d}{dx}((x + 8)^5) = 5(x + 8)^{5-1} )
Simplify the result. ( \frac{d}{dx}((x + 8)^5) = 5(x + 8)^4 )

Therefore, the derivative of ( y = (x + 8)^5 ) with respect to ( x ) is: [ \frac{d}{dx}((x + 8)^5) = 5(x + 8)^4 ]

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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.