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The text on the right side reads: **"Find the first derivative"** followed by several functions.

From what I can observe:

1. \( f(x) = x^{2} + x \)
2. \( g(x) = x^3 - 3x + 2 \)
3. \( h(x) = x^4 - 4x^2 + 7 \)
4. \( p(x) = 5x^6 - x + 1 \)
5. \( q(x) = \ln(x) \)
6. \( r(x) = e^{3x} \)

Let me differentiate each function step by step:

1. \( f'(x) = \frac{d}{dx}(x^2 + x) \)
2. \( g'(x) = \frac{d}{dx}(x^3 - 3x + 2) \)
3. \( h'(x) = \frac{d}{dx}(x^4 - 4x^2 + 7) \)
4. \( p'(x) = \frac{d}{dx}(5x^6 - x + 1) \)
5. \( q'(x) = \frac{d}{dx}(\ln(x)) \)
6. \( r'(x) = \frac{d}{dx}(e^{3x}) \)

I will now compute these derivatives.Here are the derivatives of the given functions:

1. \( f'(x) = 2x + 1 \)
2. \( g'(x) = 3x^2 - 3 \)
3. \( h'(x) = 4x^3 - 8x \)
4. \( p'(x) = 30x^5 - 1 \)
5. \( q'(x) = \frac{1}{x} \)
6. \( r'(x) = 3e^{3x} \)

Would you like further explanation on any of these derivatives or have any other questions?

Here are 5 questions related to this topic:
1. How do you find the second derivative of a function?
2. What is the geometric meaning of the first derivative?
3. How do you compute the derivative of a product of functions?
4. What is the derivative of a trigonometric function, such as \( \sin(x) \)?
5. How do you compute the derivative of implicit functions?

**Tip:** Always remember that the derivative of a sum of functions is the sum of their derivatives!

Find the first derivative of the given functions.

Learn how to calculate the first derivative for a variety of functions, including polynomials, logarithmic, and exponential expressions. This includes functions like f(x) = x^2 + x, g(x) = x^3 - 3x + 2, and r(x) = e^(3x). Suitable for high school students in Grades 11-12.

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