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Differentiation Rules

Differentiation Rules. Chain Rule Let y be a differentiable function of u and u be differentiable function of x , then The Chain Rule is sometimes stated: Let y=f(x) and u=g(x) with f differentiable at u = g(x ) and and g differentiable at x , then .

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Differentiation Rules

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  1. Differentiation Rules • Chain Rule Let y be a differentiable function of u and u be differentiable function of x, then The Chain Rule is sometimes stated: Let y=f(x) and u=g(x) with f differentiable at u= g(x) and and g differentiable at x, then

  2. Standard functions and their derivatives

  3. Examples Problems

  4. Implicit Differentiation

  5. Example • A rocket is launched vertically. Radar is 5 km from launch site. When rocket is 13 km from radar this distance is increasing at 100 km/sec. Find rocket speed. • Let y = height of rocket, s = distance from rocket to radar • Must find dy/dt.

  6. Different version • Rocket launched vertically 5 km from tracking station. When angle of elevation  = 60, the rate of change of  is 3/sec. What is the velocity at that instant (dy/dt)? Remember:  = 60 = /3 radians

  7. Derivatives of Inverse Functions • Let • Example: Find dy/dx if y = xx . Hint: ln y = ln (xx ) = x ln x.

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