What is the derivative of: f(x) = 3 f(x) = a^x f(x) = e^x f(x) = 2x^5 + 8x^3 - 3x

Hello!

Here are some differentiation rules to follow when trying to find the derivative of any function:

Now, let's find the derivative of these functions.

a). f(x) = 3 → f'(x) = 0

If you are differentiating a number, then the derivative is zero.

b). f(x) = a^x → f'(x) = a^x㏑(a)

c). f(x) = e^x → f'(x) = e^x

Looking at this, your first instinct would be to include ln(e). But, the natural log of e is ALWAYS equal to one. So, you would multiply e^x by 1, which is equal to e^x.

d). 2x^5 + 8x^3 - 3x → f'(x) = 10x^4 + 24x^2 - 3

With this, you multiply the power by the coefficient, and the power is reduced by 1. Also, the derivative of a variable is also equal to one.

2x^5: 5 x 2 = 10, 5 - 1 = 4 | 8x^3: 3 x 8 = 24, 3 - 1 = 2

Final answers:

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.