Question

Find ′ (1) and ′ (2) from the following functions:

(a) (x) = 18x
(b) (x) = cx3
(c) (x) = −5x −2
(d) (x) = 3 4 x 4/3
(e) () = 6 1/3
(f) () = −3 −1/6

Answer 1

To find the derivatives of the given functions, differentiate each function with respect to x.

Step-by-step explanation:

In calculus, a derivative measures how a function changes as its input (variable) changes. Geometrically, it represents the slope of the tangent line to the graph of the function at a given point.

To find the derivatives of the given functions, we need to differentiate them with respect to x. Let's go through each function:

1. (a) f'(x) = 18
2. (b) f'(x) = 3cx^2
3. (c) f'(x) = -5
4. (d) f'(x) = 4x^{-2/3}
5. (e) f'(x) = 0
6. (f) f'(x) = -1/6