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2028747581's Question
Math
Posted 8 months ago
Compute the derivative of the function f(x)=x2+3x+5f(x) = x^2 + 3x + 5.
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Answer from Sia
Posted 8 months ago
Solution by Steps
step 1
To find the derivative of the function f(x)=x2+3x+5f(x) = x^2 + 3x + 5, we will apply the power rule to each term
step 2
The derivative of x2x^2 with respect to xx is 2x2x
step 3
The derivative of 3x3x with respect to xx is 33
step 4
The derivative of the constant 55 with respect to xx is 00
step 5
Combining the derivatives from the previous steps, we get the derivative of the function: f(x)=2x+3f'(x) = 2x + 3
Answer
f(x)=2x+3f'(x) = 2x + 3
Key Concept
Power Rule for Differentiation
Explanation
The power rule states that the derivative of xnx^n with respect to xx is nxn1nx^{n-1}. Applying this rule to each term in the function f(x)=x2+3x+5f(x) = x^2 + 3x + 5 gives us the derivative f(x)=2x+3f'(x) = 2x + 3.

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