Mathematics

Mathematics

Problem

Calculate f′(2)f'(2) for the function f(x)=3x+1x2+4f(x)=\dfrac{3x+1}{x^{2}+4}.
Intuitive explanation

The key here is the quotient rule: when you have a fraction of two functions, the derivative is u′v−uv′v2\frac{u'v - uv'}{v^2}. Identify your numerator uu and denominator vv, find each of their derivatives, plug into the formula, then evaluate at x=2x=2. This is a straightforward application—just careful algebra.

Intuitive explanation

The key here is the quotient rule: when you have a fraction of two functions, the derivative is u′v−uv′v2\frac{u'v - uv'}{v^2}. Identify your numerator uu and denominator vv, find each of their derivatives, plug into the formula, then evaluate at x=2x=2. This is a straightforward application—just careful algebra.

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