Example: sin(10t) | Massachusetts Institute of Technology - Edubirdie

University:
Massachusetts Institute of Technology
Course:
18.01SC | Single Variable Calculus
Academic year:

2024
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495

Pages:

1
Author:

Cejass4

Example: sin(10t) dy dx The chain rule (composition rule) says that dy dt = dx dt . In other words, the derivative of the composition of functions f (g(t)) is the derivative of the outside function f (x) times the derivative of the inside function g(t). d For the example dt sin(10t), the inside function is x = 10t and the outside dy function is y = sin x. Using the rules we know, we can compute that dx = cos x and dx = 10, so: dt dy dy dx = = cos x · 10. dt dx dt Since we’re the only ones who know the value of x in this formula, we replace x by 10t to get: dy = cos(10t) · 10 = 10 cos(10t). dt Once you’ve had more practice using the chain rule, you won’t always need d the variable x that represents the inside function. When you look at dt sin(10t) you might say to yourself: “The derivative of the outside function, sine, is cosine. I’m plugging 10t into it. And the derivative of 10t is just 10. So d dt sin(10t) = cos(10t) · 10.

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