SOLUTION: How do I differentiate y=sin^3x?

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Question 969163: How do I differentiate y=sin^3x?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

If y=+sin%5E3%28x%29
it is same as
y=+%28sinx%29%5E3
let sin%28x%29=+u, then du%2Fdx+=cos%28x%29
and y=+u%5E3, then dy%2Fdu=3u%5E2
using chain rule
dy%2Fdx=%28dy%2Fdu%29+%2A%28du%2Fdx%29
=>+dy%2Fdx=+3u%5E2+%2A+cosx
recall that u=+sin%28x%29
=>+dy%2Fdx=+3%28sin%28x%29%29%5E2+%2A+cos%28x%29
=>dy%2Fdx=+3sin%5E2%28x%29cos%28x%29