Adam C.
asked • 09/13/20Calculus chain rule and trigonometric functions
Calculus Question:
In the following equation, a and b are constants, and E is a function of the variable t. Find expressions for dx/dt in terms of a, b, E and dE/dt.
x = a cos E
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1 Expert Answer
Shaun L. answered • 09/13/20
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Physics and Applied Math Student at Yale University
First, differentiate the entire equation with respect to t. We need to remember the derivatives of trig functions and that since E is a function of t, we need to apply the chain rule.
dx/dt = - a sin E * dE/dt
Adam C.
Thanks Shaun, would you mind putting the steps in, just so it is clear I’m my mind, as a previous answer I saw was asinE*dE/dt. Thanks in advance.
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09/14/20
Shaun L.
Sure, no problem. From left to right, we'll take the derivative of the equation with respect to t. Differentiating x, we get simply dx/dt. On the other side of the equation, a is a constant and gets pulled out to the front of everything else. The derivative of d/dt(cos y) is - sin y. In this case, the "y" is our E, which is also a function of t. So, applying the chain rule, we take the derivative of cos E as -sin E multiplied by the derivative of E with respect to t. So our final answer is dx/dt = - a sin E * dE/dt.
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09/14/20
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Adam C.
I have a solution of: a sin E dE/dt, but shouldn’t the solution be: -a sin E dE/dt?09/13/20