Of course, there are many angles with the same sine, so the sine function doesn't actually have an inverse that reliably "undoes'' the sine function. Calculus of a Single Variable (AP Edition). 4.9: Inverse Trigonometric Functions The trigonometric functions frequently arise in problems, and often it is necessary to invert the functions, for example, to find an angle with a specified sine. Every edition from the first to the seventh of CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS has made the mastery of traditional calculus skills a priority, while embracing the best features of new technology and, when appropriate, calculus reform ideas. Calculus of a Single Variable: Early Transcendental Functions (AP® Edition).Fresh features from the 1 AI-enhanced learning platform. By using implicit differentiation, we can find the equation of a tangent line to the graph of a curve. Find step-by-step solutions and answers to Calculus: Early Transcendental Functions - 9781337552516, as well as thousands of textbooks so you can move forward with confidence. 4.8: Implicit Differentiation We use implicit differentiation to find derivatives of implicitly defined functions (functions defined by equations).4.7: Derivatives of the Exponential and Logarithmic Functions As with the sine, we do not know anything about derivatives that allows us to compute the derivatives of the exponential and logarithmic functions without going back to basics.The logarithmic functions are the inverses of the exponential functions, that is, functions that "undo'' the exponential functions. 4.6: Exponential and Logarithmic Functions An exponential function has the form \(a^x\), where \(a\) is a constant.4.5: Derivatives of the Trigonometric Functions All of the other trigonometric functions can be expressed in terms of the sine, and so their derivatives can easily be calculated using the rules we already have.4.4: The Derivative of sin x - II Now we can complete the calculation of the derivative of the sine.4.1: Trigonometric Functions Although the trigonometric functions are defined in terms of the unit circle, the unit circle diagram is not what we normally consider the graph of a trigonometric function.
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