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Find the derivatives of the following (1...

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

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To find the derivative of the function \( f(x) = 2x - \frac{3}{4} \), we will follow the rules of differentiation step by step. ### Step 1: Identify the function The given function is: \[ f(x) = 2x - \frac{3}{4} \] ### Step 2: Differentiate each term We will differentiate each term of the function separately. 1. The first term is \( 2x \). - The derivative of \( 2x \) with respect to \( x \) is \( 2 \). This is because the derivative of \( ax \) (where \( a \) is a constant) is \( a \). 2. The second term is \( -\frac{3}{4} \). - The derivative of a constant is \( 0 \). Therefore, the derivative of \( -\frac{3}{4} \) is \( 0 \). ### Step 3: Combine the derivatives Now, we combine the derivatives of both terms: \[ f'(x) = 2 + 0 = 2 \] ### Final Answer Thus, the derivative of the function \( f(x) = 2x - \frac{3}{4} \) is: \[ f'(x) = 2 \]
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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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