C'mon TKHunny, remember that some people are not as smart as you.
Originally Posted by
marikas 2. Differentiate the following functions with respect to y = 3 sin(2x)
Hint: Use the chain–rule with
u = 2x.
For letter a), you need to know that $\displaystyle (x^n)'=nx^{n-1},$ for $\displaystyle n$ a rational number.
For letter b), I'll use two ways:
$\displaystyle y'=3\cos(2x)\cdot(2x)'=3\cos(2x)\cdot2=6\cos2x.$
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Define $\displaystyle u=2x\implies u'=2.$ Since $\displaystyle y=3\sin u\implies y'=3\cos u\cdot u'.$
Now back substitute
$\displaystyle y'=3\cos2x\cdot2=6\cos2x.$
Hope it helps