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

Break Down the Problem

1. Identify the function to differentiate: $y = \tan(5x - 4)$.
2. Recognize the need to apply the chain rule for differentiation since the function is a composite function.

Relevant Concepts

3. The derivative of $\tan(u)$ with respect to $u$ is $\sec^2(u)$.
4. Apply the chain rule: If $y = \tan(u)$, then $\frac{dy}{dx} = \sec^2(u) \cdot \frac{du}{dx}$, where $u = 5x - 4$.

Analysis and Detail

5. Compute $\frac{du}{dx}$: $u = 5x - 4 \implies \frac{du}{dx} = 5$
6. Now, substitute back into the derivative: $\frac{dy}{dx} = \sec^2(5x - 4) \cdot 5$

Verify and Summarize

7. Thus, the derivative is: $\frac{dy}{dx} = 5 \sec^2(5x - 4)$

Final Answer

The correct answer is $5 \sec^2(5x - 4)$.