Question

Math

Posted 6 months ago

`Compute the derivative of the function $f(x) = x^2 + 3x + 5$.`

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Answer from Sia

Posted 6 months ago

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 $x$ is $2x$

step 3

The derivative of $3x$ with respect to $x$ is $3$

step 4

The derivative of a constant, $5$, with respect to $x$ is $0$

step 5

Combining the derivatives from steps 2, 3, and 4, we get $2x + 3 + 0$

step 6

Simplifying the expression from step 5, 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 $x^n$ with respect to $x$ is $nx^{n-1}$. Applying this rule to each term in the function $f(x)$ gives us the derivative.

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