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Find \cot \theta, given that \cos \theta = -\frac{2}{3} and \theta is in Quadrant III. Show all work without a calculator. Simplify and find the exact value of cot( 1/2 tan^{-1} 2). Assume x is greater than 0. Rationalize denominators. ...
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Find the following limit: {eq}\lim_{x \to -1} \frac{3 + 2x}{2x - 2} {/eq} Limits: The limit is a particular value to which a function approaches as the input of that function approaches a given value (in the above question, we need to find the limit of the functi...
Derivatives of Inverse Functions Function must be one-to-one If f is differentiable at every point of an interval and df/dx is never zero on the interval, then f has an inverse and f -1 is differentiable at every point. Derivative of arcsin...
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Find {eq}\frac{dy}{dx} {/eq} for the function implicitly defined by the equation {eq}x + x^2= \sin y {/eq}Implicit Differentiation:We can categorize the differentiation of functions in two ways- explicit or implicit differentiation. Implicit differentiation entails ...
We will have to use implicit differentiation twice to find the wanted derivative. Recall that implicit differentiation is a rather unnecessary name for a direct application of the chain rule. All we are really doing here is taking a couple derivatives and applying the chain rul...
The differentiation of the function can be easily found using the standard formula. There is another method to find the derivative, that is by the use of the first principle rule of differentiation, we need to use the concepts of limits ...
Differentiation is the process of finding the derivative of a function. Usually, differentiation can be done explicitly. However, if we are given an implicit equation or function, we may need to use implicit differentiation. Answer and Explanation: Solution (a): Here the give...