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What is the derivative of $y=4x^{2}+\cot x$ ?

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Solve complex trigonomentric equations

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Q. What is the derivative of

y=4x^{2}+\cot x

?

Identify Function Components: Identify the function components to differentiate. $\newline$ The function $y = 4x^2 + \cot(x)$ consists of two terms: $4x^2$ and $\cot(x)$ . We will differentiate each term separately.
Differentiate First Term: Differentiate the first term $4x^2$ with respect to $x$ . Using the power rule, the derivative of $x^n$ with respect to $x$ is $n*x^{(n-1)}$ , so the derivative of $4x^2$ is $4*2*x^{(2-1)} = 8x$ .
Differentiate Second Term: Differentiate the second term $\cot(x)$ with respect to $x$ . The derivative of $\cot(x)$ with respect to $x$ is $-\csc^2(x)$ , where $\csc(x)$ is the cosecant function, which is the reciprocal of the sine function.
Combine Derivatives: Combine the derivatives of both terms to find the derivative of the entire function. $\newline$ The derivative of $y = 4x^2 + \cot(x)$ is the sum of the derivatives of its terms, which is $8x - \csc^2(x)$ .

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