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There are multiple rules of differentiation in calculus, and each one works best in a different situation. For example, there is the product rule, quotient rule, and power rule. These work well for polynomial functions. Trigonometric functions are differentiated in their own way. Derivatives of exponential functions (for example, 7^x), are sometimes calculated by first taking the natural log of both sides of the equation y=7^x. Piecewise functions can contain multiple types of expressions, and accordingly each piece can be differentiated using a different rule. Hope this helps!
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DevinThere is only one way and that is from the definition. The derivative of a function f(x), at a point whose abscissa is p, is the limit as dx tends to zero, of [f(p+dx) - f(p)]/dx. Many of the simpler results are then taken as basic building blocks to find the derivatives of more complicated functions.
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