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Prove from first principles, that d/(dx)...

Prove from first principles, that `d/(dx)(alphax^(n))=alphanx^(n-1)`.

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MODERN PUBLICATION-LIMITS AND DERIVATIVES-EXERCISE 13 (e)
  1. Find the derivatives of the following (1-3) functions : f(x) = a

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  2. Find the derivatives of the following (1-3) functions : f(x) = pi

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  3. Find the derivatives of the following (1-3) functions : f(x) = x+a

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  4. Find the derivatives of the following (1-3) functions : f(x)=(ax+b)^...

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  5. Find the derivatives of the following (1-3) functions : f(x)=2x-3/4

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  6. Find the derivatives of the following (1-3) functions : f(x)=x^(3)+4...

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  7. Find the derivatives of the following (1-3) functions : y=x^(2)

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  8. Find the derivatives of the following (1-3) functions : y=5/2x^(7)

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  9. For each of the following functions, evaluate the derivative at the in...

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  10. For each of the following functions, evaluate the derivative at the in...

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  11. For each of the following functions, evaluate the derivative at the in...

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  12. For each of the following functions, evaluate the derivative at the in...

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  13. Find 'a' if f^(')(a)=0, where f(x)=x^(3)-3x^(2)+3x-1

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  14. If f(x)=alphax^(n), prove that alpha=(f^(')(1))/n.

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  15. Prove from first principles, that d/(dx)(alphax^(n))=alphanx^(n-1).

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  16. Use the delta method to find the derivative of f(x)=x^(4). Hence find ...

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  17. If y=1=x/(1!)+(x^2)/(2!)+(x^3)/(3!)++(x^n)/(n !), show that (dy)/(dx)-...

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