Differentiate with respect to
x

(i)
4 tan , x x

To differentiate the expression \( 4 \tan(x) \) with respect to \( x \), we'll apply the standard differentiation rules.

### Given expression:
\[
y = 4 \tan(x)
\]

### Differentiating with respect to \( x \):

\[
\frac{dy}{dx} = 4 \cdot \frac{d}{dx} [\tan(x)]
\]

The derivative of \( \tan(x) \) is \( \sec^2(x) \). So,

\[
\frac{dy}{dx} = 4 \sec^2(x)
\]

### Final result:
\[
\frac{d}{dx} [4 \tan(x)] = 4 \sec^2(x)
\]

Would you like further details or have any questions?

Here are 5 related questions for you:
1. What is the derivative of \( \sec(x) \) with respect to \( x \)?
2. Can you differentiate \( \tan^2(x) \) with respect to \( x \)?
3. How would you differentiate \( \tan(x^2) \) with respect to \( x \)?
4. How do

Differentiate with respect to x: 4 tan(x)

Learn how to differentiate the trigonometric function 4 tan(x) with respect to x using standard differentiation rules. This solution covers key calculus concepts, including the derivative of tan(x) and the application of sec^2(x). Suitable for students in Grades 11-12.

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