The equation of a curve is $$\(y=\sqrt{\tan x}\)$$, for $$\(0 \leqslant x<\frac{1}{2} \pi\)$$. Express $$\(\frac{\mathrm{d} y}{\mathrm{~d} x}\)$$ in terms of $$\(\tan x\)$$, and verify that $$\(\frac{\mathrm{d} y}{\mathrm{~d} x}=1\)$$ when $$\(x=\frac{1}{4} \pi\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_w21_qp_32 Year：2021 Question No：11(a)
Answer:
Use chain rule
Obtain correct derivative in any form
Use correct Pythagoras to obtain correct derivative in terms of \(\tan x\)
Use a correct derivative to obtain \(\frac{\mathrm{d} y}{\mathrm{~d} x}=1\) when \(x=\frac{1}{4} \pi\)
Obtain correct derivative in any form
Use correct Pythagoras to obtain correct derivative in terms of \(\tan x\)
Use a correct derivative to obtain \(\frac{\mathrm{d} y}{\mathrm{~d} x}=1\) when \(x=\frac{1}{4} \pi\)
Knowledge points:
3.3.1 understand the relationship of the secant, cosecant and cotangent functions to cosine, sine and tangent, and use properties and graphs of all six trigonometric functions for angles of any magnitude
3.4.1 use the derivatives of together with constant multiples, sums, differences and composites (Derivatives of are not required.)
Solution:
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