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derivative of $2 \sin x + \frac{3}{\cos x}$

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Solve two-step linear inequalities

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Q. derivative of

2 \sin x + \frac{3}{\cos x}

Find Derivative of $2$ sin(x): We need to find the derivative of the function $f(x) = 2 \sin(x) + \frac{3}{\cos(x)}$ . We will use the sum rule for derivatives, which states that the derivative of a sum is the sum of the derivatives. We will also use the derivative rules for sine and cosine functions.
Find Derivative of $3$ /cos(x): First, let's find the derivative of the first term, $2 \sin(x)$ . The derivative of $\sin(x)$ with respect to $x$ is $\cos(x)$ , so the derivative of $2 \sin(x)$ is $2 \cos(x)$ .
Combine Derivatives for f(x): Now, let's find the derivative of the second term, $\frac{3}{\cos(x)}$ . This is the same as $3 \sec(x)$ , where $\sec(x)$ is $\frac{1}{\cos(x)}$ . The derivative of $\sec(x)$ with respect to $x$ is $\sec(x) \tan(x)$ , so the derivative of $3 \sec(x)$ is $3 \sec(x) \tan(x)$ .
Combine Derivatives for f(x): Now, let's find the derivative of the second term, $\frac{3}{\cos(x)}$ . This is the same as $3 \sec(x)$ , where $\sec(x)$ is $\frac{1}{\cos(x)}$ . The derivative of $\sec(x)$ with respect to $x$ is $\sec(x) \tan(x)$ , so the derivative of $3 \sec(x)$ is $3 \sec(x) \tan(x)$ .Combining the derivatives of both terms, we get the derivative of the function $f(x)$ as $3 \sec(x)$ $0$ .

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