How do you use the limit definition to find the derivative of $f (x) = 3 x^{\frac{2}{3}} - 4 x^{\frac{1}{2}} - 2$ $f(x)=3x^(2/3)-4x^(1/2)-2$ ?

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Answer 1 · 2017-01-20T14:36:35

I would first use the limit definition to show that the derivative of a sum is the sum of the derivatives.

Then I could use the definition to show that

the derivative of $3 x^{\frac{2}{3}}$ $3x^(2/3)$ is $2 x^{- \frac{1}{3}}$ $2x^(-1/3)$ and

the derivative of $- 4 x^{\frac{1}{2}}$ $-4x^(1/2)$ is $- 2 x^{- \frac{1}{2}}$ $-2x^(-1/2)$ and

the derivative of $- 2$ $-2$ is $0$ $0$ .

Therefore the derivative of $f (x)$ $f(x)$ is

$2 x^{- \frac{1}{3}} - 2 x^{- \frac{1}{2}}$ $2x^(-1/3) -2x^(-1/2)$

How do you use the limit definition to find the derivative of f(x)=3x^(2/3)-4x^(1/2)-2f(x)=3x23−4x12−2f(x)=3x^(2/3)-4x^(1/2)-2?