Differentiate the function y = tan(5x-4)

Differentiate the function y = tan(5x-4)Question 10Select one:5 sec^2 (5x-4)2x+13y20(4𝑥-3)415(3x+2)

Evaluate the derivative of the function y= 5 sin⁡x + 2 cos⁡x

To obtain the derivative of  y = (2x4 + 1)tan xWe utilize the following steps. Arrange the order to obtain the solution.

find derivative of tan x at x=2

To find the derivative of \( 5 \tan(\ln x) \), we will use the chain rule. Let \( u = \ln x \). Then, the function becomes \( 5 \tan(u) \). First, find the derivative of \( 5 \tan(u) \) with respect to \( u \): \[ \frac{d}{du} [5 \tan(u)] = 5 \sec^2(u) \] Next, find the derivative of \( u = \ln x \) with respect to \( x \): \[ \frac{du}{dx} = \frac{1}{x} \] Now, apply the chain rule: \[ \frac{d}{dx} [5 \tan(\ln x)] = 5 \sec^2(\ln x) \cdot \frac{1}{x} \] So, the derivative is: \[ \frac{5 \sec^2(\ln x)}{x} \] Therefore, the correct answer is: \[ \boxed{C} \]