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Compute the derivative of the function

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

Mar 26, 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

2x

by the power rule

step 3

The derivative of

3x

3

as the derivative of

x

1

and

3

is a constant multiplier

step 4

The derivative of the constant

5

0

since the derivative of any constant is

0

step 5

Combining the derivatives from the previous steps, we get

2x + 3 + 0

step 6

Simplifying, we have

2x + 3

as the derivative of the function

f(x)

Answer

The derivative of the function

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

2x + 3

Key Concept

Power Rule for Differentiation

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)

and adding the results gives us the derivative of the entire function.