4.0
6.5
5.0
10.6
Correct answer is B
f(x)=(x2+3)2
Using the chain rule, dydx=dydu×dudx
Let u=x2+3 so that y=u2
dydu=2u
dudx=2x
∴
But u = x^{2} + 3,
\frac{\mathrm d y}{\mathrm d x} = 4x(x^{2} + 3)
At x = \frac{1}{2}, \frac{\mathrm d y}{\mathrm d x} = 4(\frac{1}{2})((\frac{1}{2})^{2} + 3)
= 2 \times \frac{13}{4} = \frac{13}{2} = 6.5
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