JAMB - Mathematics (2014 - No. 30)
If y = cos 3x, find \(\frac{\delta y}{\delta x}\)
\(\frac{1}{3} \sin 3x\)
\(-\frac{1}{3} \sin 3x\)
3 sin 3x
-3 sin 3x
설명
y = cos 3x
Let u = 3x so that y = cos u
Now, \(\frac{\delta y}{\delta x} = 3\),
\(\frac{\delta y}{\delta x} = -sin u\)
By the chain rule,
\(\frac{\delta y}{\delta x} = \frac{\delta y}{\delta u} \times \frac{\delta u}{\delta x}\)
\(\frac{\delta y}{\delta x} = (-\sin u) (3)\)
\(\frac{\delta y}{\delta x} = -3 \sin u\)
\(\frac{\delta y}{\delta x} = -3 \sin 3x\)
Let u = 3x so that y = cos u
Now, \(\frac{\delta y}{\delta x} = 3\),
\(\frac{\delta y}{\delta x} = -sin u\)
By the chain rule,
\(\frac{\delta y}{\delta x} = \frac{\delta y}{\delta u} \times \frac{\delta u}{\delta x}\)
\(\frac{\delta y}{\delta x} = (-\sin u) (3)\)
\(\frac{\delta y}{\delta x} = -3 \sin u\)
\(\frac{\delta y}{\delta x} = -3 \sin 3x\)