Find derivative of sec x cot x

April 5, 2026Mathematics

ScanSolve AI Answer

April 5, 2026

Answer

-\csc x \cot x

Let the function be $f(x) = \sec x \cot x$ .

Step 1: Simplify the function using trigonometric identities. We know that $\sec x = \frac{1}{\cos x}$ and $\cot x = \frac{\cos x}{\sin x}$ . $f(x) = \frac{1}{\cos x} \cdot \frac{\cos x}{\sin x}$ $f(x) = \frac{1}{\sin x}$ $f(x) = \csc x$

Step 2: Find the derivative of the simplified function. The derivative of $\csc x$ is $-\csc x \cot x$ . $\frac{d}{dx}(\csc x) = -\csc x \cot x$

Therefore, the derivative of $\sec x \cot x$ is: $\boxed{-\csc x \cot x}$

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Let the function be f(x) = x x. Step 1: Simplify the function using trigonometric identities.

Asked on April 5, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 5, 2026

Let the function be f(x) = x x. Step 1: Simplify the function using trigonometric identities. We know that x = (1)/( x) and x = ( x)/( x). f(x) = (1)/( x) · ( x)/( x) f(x) = (1)/( x) f(x) = x Step 2: Find the derivative of the simplified function. The derivative of x is - x x. (d)/(dx)( x) = - x x Therefore, the derivative of x x is: x x