The equation of a curve is $$\(\cos 3 x+5 \sin y=3\)$$. Find the gradient of the curve at the point $$\(\left(\frac{1}{9} \pi, \frac{1}{6} \pi\right)\)$$. ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................
Exam No：9709_s20_qp_22 Year：2020 Question No：3
Answer:
Differentiate \(\cos 3 x\) to obtain \(-3 \sin 3 x\)
Differentiate \(5 \sin y\) to obtain \(5 \cos y \frac{\mathrm{d} y}{\mathrm{~d} x}\)
Obtain \(-3 \sin 3 x+5 \cos y \frac{\mathrm{d} y}{\mathrm{~d} x}=0 \quad \mathrm{OE}\)
Substitute \(x\) and \(y\) values to find value of first derivative
\(\operatorname{Obtain} \frac{3}{5}\)
Differentiate \(5 \sin y\) to obtain \(5 \cos y \frac{\mathrm{d} y}{\mathrm{~d} x}\)
Obtain \(-3 \sin 3 x+5 \cos y \frac{\mathrm{d} y}{\mathrm{~d} x}=0 \quad \mathrm{OE}\)
Substitute \(x\) and \(y\) values to find value of first derivative
\(\operatorname{Obtain} \frac{3}{5}\)
Knowledge points:
2.4.3 find and use the first derivative of a function which is defined parametrically or implicitly.
Solution:
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