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Math 3A Midterm II Review

# Math 3A Midterm II Review - Math Midterm II Review Math...

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Math Midterm II Review Math 3A/AAP Tutorials Jenese Ortiz Math 3A Midterm II Review I. Implicit Differentiation a. Differentiate both sides of equation with respect to x, keeping in ind that y is function of x b. Always solve for dy/dx II. Derivatives of Trig Fxns a. d/dx sinx= b. d/dx tanx= c. d/dx secx= d. d/dx cosx= e. d/dx cotx= f. d/dx cscx= III. Exponential Functions a. d/dx e^g(x)= b. d/dx a^g(x)= Examples: Find dy/dx of: 1. y=e^(sin(x^2-1)) 2. y=e^(xsinx) 3. y=5^sqrt(x) 4. y=3^(x^3-1) 5. y=e^e^x 6. y=cos(e^(pix)) 7. cos(x-y)=xe^x

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8. y=(e^x+e^-x)/(e^x-e^-x) IV. Related Rates 1. Related Rates: ALWAYS take the derivative with respect to TIME (ex: dSA/dt, dV/dt, dr/dt). Note: Related Rates are a type of implicit differentiation . Example: 2. A television camera is positioned 4000 ft from the base of rocket launching pad. The angle of elevation of the camera has to change at the correct rate in order to keep the rocket in sight. Also, the mechanism for focusing the camera has to take into account the increasing distance from the camera to the rising rocket. Let’s assume the rocket rises vertically and
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Math 3A Midterm II Review - Math Midterm II Review Math...

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