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Find the differential dy of y=cos(x)

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Final Answer

$dy=-\sin\left(x\right)$

Step-by-step Solution

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Math interpretation of the question

$\frac{d}{dx}\left(y=\cos\left(x\right)\right)$

Learn how to solve implicit differentiation problems step by step online.

$\frac{d}{dx}\left(y=\cos\left(x\right)\right)$

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Learn how to solve implicit differentiation problems step by step online. Find the differential dy of y=cos(x). Math interpretation of the question. Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of the linear function is equal to 1. The derivative of the cosine of a function is equal to minus the sine of the function times the derivative of the function, in other words, if f(x) = \cos(x), then f'(x) = -\sin(x)\cdot D_x(x).

Final Answer

$dy=-\sin\left(x\right)$

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Main Topic: Implicit Differentiation

Implicit differentiation makes use of the chain rule to differentiate implicitly defined functions. For differentiating an implicit function y(x), defined by an equation R(x, y) = 0, it is not generally possible to solve it explicitly for y(x) and then differentiate. Instead, one can differentiate R(x, y) with respect to x and y and then solve a linear equation in dy/dx for getting explicitly the derivative in terms of x and y.

Used Formulas

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