- #1

- 16

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Find this derivative algebraically

f(x) = x^3 (x cubed) at x= -2

The answer in the back of the book says the derivative is 12 - but I did the work and got 4. Please help!

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- Thread starter dec1ble
- Start date

- #1

- 16

- 0

Find this derivative algebraically

f(x) = x^3 (x cubed) at x= -2

The answer in the back of the book says the derivative is 12 - but I did the work and got 4. Please help!

- #2

quasar987

Science Advisor

Homework Helper

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Thy shalt not forget to multiply by the exponent... i.e.

[tex](x^a)' = ax^{a-1}[/tex]

[tex](x^a)' = ax^{a-1}[/tex]

- #3

- 1,235

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Do the same for your function

- #4

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[tex] D=:\lim_{x\rightarrow -2}\frac{f(x)-f(-2)}{x-(-2)}=\lim_{x\rightarrow -2}\frac{x^{3}+8}{x+2}=\lim_{x\rightarrow -2} x^{2}-2x+4 =+12 [/tex]

,where i made use of the identity:

[tex] a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2}) [/tex]

Daniel.

- #5

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[tex]y=x^3~~n=3[/tex]

if you have a polynomial function, and you want to find the derivative of it use the fact that if [itex]y=x^n[/itex], then [itex]\frac{dy}{dx} = nx^{n-1}[/itex].

[tex]\frac{dy}{dx}=3x^{3-1}=3x^2[/tex]

now, evaluate [itex]3x^2[/itex] at -2.

[tex]\frac{dy}{dx}=3(-2)^2=3(4)=12[/tex]

that's the lazy way.

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