The equation of a curve is $$\(y=2 x+1+\frac{1}{2 x+1}\)$$ for $$\(x>-\frac{1}{2}\)$$. Find $$\(\frac{\mathrm{d} y}{\mathrm{~d} x}\)$$ and $$\(\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_w20_qp_13 Year：2020 Question No：8(a)
Answer:
\(\frac{\mathrm{d} y}{\mathrm{~d} x}=[2] \quad\left[-2(2 x+1)^{-2}\right]\)
\(\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}=8(2 x+1)^{-3}\)
\(\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}=8(2 x+1)^{-3}\)
Knowledge points:
1.7.1 understand the gradient of a curve at a point as the limit of the gradients of a suitable sequence of chords, and use the notations for first and second derivatives (Only an informal understanding of the idea of a limit is expected.)
1.7.2 use the derivative of (for any rational ), together with constant multiples, sums and differences of functions, and of composite functions using the chain rule
Solution:
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