prove that derivative of cos(x) is -sin(x)

Introduction : In this we shall prove that the derivative of cos(x) is -sin(x) using the formal definition of derivative.Question : prove that derivative of cos(x) is -sin(x)Solution :\[f\left(x\right)=\cos{\left(x\right)}\]Derivative of a function is defined as\[\frac{df\left(x\right)}{dx}=limit_{∆x→0}\frac{f(x+∆x)-f(x)}{x+∆x-x}\]Using the definition of f(x)\[=limit_{∆x→0}\frac{cos(x+∆x)-cos(x)}{∆x}\]By the…

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