Mathematics·Derivative·grades 10–11

Find the derivative of the function f(x) = x² + 3x

Problem

The function f(x) = x² + 3x is given. Find its derivative f′(x).

Answer

f′(x) = 2x + 3

Step-by-step solution

Step 1. Recall the rule
The derivative of a sum equals the sum of the derivatives: $(u+v)' = u' + v'$ . So we differentiate each term separately.
Step 2. Derivative of the first term
For a power function $(x^n)' = n\,x^{n-1}$ . Therefore $(x^2)' = 2x$ .

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Step 3. Derivative of the second term
Step 4. Assemble the answer

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Common mistakes

Forgetting that the derivative of a constant is zero (there is no constant here, but in f(x)=x²+3x+5 the term 5 disappears).
Writing $(x^2)' = x$ instead of $2x$ — losing the factor from the exponent.

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