Question 1 1 Let fxx2 Note the symbol denotes an exponent T

Question 1 1

Let f(x)=x^2 (Note: the ^ symbol denotes an exponent). Then f\'(x) is:

2x^2

Question 2

Let f(x)=5x^2 (Note: the ^ symbol denotes an exponent). Then f\'(x) is:

Question 3

Let f(x)=10x^15. Then f\'(x) is:

Question 4

Let f(x)=3ln(x). Then f\'(x) is:

Question 5

Let f(x)=dx^c, where d and c are real numbers. Then f\'(x) is:

Question 6

The sum rule for derivatives states that the derivative of h(x)=f(x)+g(x) is h\'(x)=f\'(x)+g\'(x). Let h(x)=f(x)+g(x), where f(x)=3x and g(x)=x^2. In other words, h(x)=3x+x^2. What is h\'(x)?

Solution

1. 2x

2. 10x

3. 150x¹⁴

4. 3/x

5. cdx^{(c - 1)}

6. 3+2x