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Compute the derivative of the function

f(x) = x^2 + 3x + 5

Dec 24, 2023

Compute the derivative of the function

f(x) = x^2 + 3x + 5

Solution by Steps

step 1

To compute the derivative of the function

f(x) = x^2 + 3x + 5

, we will use the power rule for differentiation, which states that the derivative of

x^n

nx^{n-1}

step 2

Differentiating each term of the function separately:

f'(x) = \frac{d}{dx}(x^2) + \frac{d}{dx}(3x) + \frac{d}{dx}(5)

step 3

Applying the power rule to each term:

f'(x) = 2x^{2-1} + 3x^{1-1} + 0

step 4

Simplifying the expression:

f'(x) = 2x + 3

Answer

The derivative of the function

f(x) = x^2 + 3x + 5

f'(x) = 2x + 3

Key Concept

Power Rule for Differentiation

Explanation

The power rule for differentiation is used to find the derivative of each term in the polynomial function

f(x) = x^2 + 3x + 5

, resulting in

f'(x) = 2x + 3