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Find the derivative of $f(x)=3x$ at $x=2$

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Find values of derivatives using limits

Full solution

Q. Find the derivative of

f(x)=3x

at

x=2

Identify Function & Point: Identify the function and the point at which we need to find the derivative. We are given the function $f(x) = 3x$ and we need to find its derivative at $x = 2$ .
Recall Power Rule: Recall the power rule for differentiation. The power rule states that the derivative of $x^n$ with respect to $x$ is $n*x^{(n-1)}$ . In our case, the function is $3x$ , which is $3*x^1$ .
Apply Power Rule: Apply the power rule to find the derivative of $f(x) = 3x$ . $\newline$ Using the power rule, the derivative of $3x$ with respect to $x$ is $3\times 1\times x^{1-1} = 3\times x^0 = 3$ .
Evaluate at $x = 2$ : Evaluate the derivative at $x = 2$ . $\newline$ Since the derivative of $f(x) = 3x$ is a constant $3$ , it does not change with $x$ . Therefore, the derivative at $x = 2$ is also $3$ .

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