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Derivatives are often the first concept that is taught in Calculus. Understanding how to find the derivative of a function is essential to your success in the course. The article below provides details on the five basic methods used. <\/span><\/p>\n The power rule provides a method for taking the derivative of any polynomial function. <\/span><\/p>\n When doing so, we consider each algebraic term separately, applying the following rule: <\/span><\/p>\n The derivative of \u00a0y = ax^b is y\u2019 = \u00a0\u00a0a*bx^(b-1) <\/span><\/p>\n Keep in mind that terms without variables are constant so their rate of change is zero and therefore their derivative is defined as 0. <\/span><\/p>\n Example: <\/b>\u00a0The derivative of \u00a0\u00a03x^3 + 6x^2 – 3x + 10 \u00a0\u00a0is 9x^2 + 12x – 3 <\/span> \u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n Pro Tip: <\/b>Remember that irrational numbers represented by symbols, like \u213c and e, are still constants and therefore their derivative is 0.<\/span><\/p>\n The product rule provides a method for taking the derivative of a function created by the multiplication of two functions. We use the following formula:<\/span><\/p>\n The derivative of \u00a0\u00a0f(x) = g(x)h(x) becomes \u00a0\u00a0\u00a0f\u2019(x) = g(x)h\u2019(x) + g\u2019(x)h(x) \u00a0<\/span><\/p>\n where g\u2019(x) and h\u2019(x) are the derivatives of g(x) & h(x) \u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n Example: <\/b>The derivative of \u00a0\u00a0\u00a0(2x^2 – 1)(x^4 – 2) is \u00a0\u00a04x(x^4 – 2) + (2x^2 – 1)(4x^3) <\/span><\/p>\n which can be simplified to 12x^5 – 4x^3 – 8x<\/span><\/p>\n The three basic trigonometric functions are sin(x), cos(x), and tan(x). The best way to handle the derivatives of these functions is to memorize them. <\/span><\/p>\n\n
Power Rule<\/b><\/h4>\n<\/li>\n<\/ul>\n
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Product Rule <\/b><\/h4>\n<\/li>\n<\/ul>\n
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Derivatives of Basic Trig Functions<\/b><\/h4>\n<\/li>\n<\/ul>\n