In calculus, the way you solve a derivative problem depends on what form the problem takes. Common problem types include the chain rule; optimization; position, velocity, and acceleration; and related rates. Here are a few things to remember when solving each type of problem:
Chain Rule problems
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Use the chain rule when the argument of the function you’re differentiating is more than a plain old x.
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Work from outside, in.
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Don’t touch the inside stuff.
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Do only one derivative per step.
Optimization problems
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Express the thing you want to minimize or maximize as a function of the unknown.
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Differentiate and set the derivative equal to zero.
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Solve and plug the solution into the original function.
Position, velocity, and acceleration problems
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The derivative of position is velocity and the antiderivative of velocity is position.
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The derivative of velocity is acceleration and the antiderivative of acceleration is velocity.
Related rates problems
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Assign variables to changing quantities, but not to unchanging things.
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Differentiate before plugging in variable values.
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Use the Pythagorean Theorem for right triangle problems and use similar triangles for problems involving cones or shapes that have a triangular cross-section.