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Compute the derivative of the function

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

Mar 11, 2024

Compute the derivative of the function

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

Generated Graph

Solution by Steps

step 1

To find the derivative of the function

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

, we will apply the power rule to each term

step 2

The derivative of

x^2

with respect to

x

2x

step 3

The derivative of

3x

with respect to

x

3

step 4

The derivative of a constant, such as

5

, is

0

step 5

Combining the derivatives from steps 2, 3, and 4, we get

2x + 3 + 0

step 6

Simplifying the expression, we have

2x + 3

Answer

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

Key Concept

Differentiation using the power rule

Explanation

The power rule states that the derivative of

x^n

nx^{n-1}

. Applying this rule to each term in the function

f(x)

gives us the derivative. Constants have a derivative of zero.