Differentiate the following functions using the differentiation formulas

1). f(x)=3
2). f(x)=8x²
3). f(x)=x^3/2
4). f(x) x^n
5). f(x)=cx^n
6). f(x)=π
7). f(x)=6x^-3
8). f(x)=√x
9). f(x)=2x+5
10). f(x)=2+√x

Question

Differentiate the following functions using the differentiation formulas

1). f(x)=3
2). f(x)=8x²
3). f(x)=x^3/2
4). f(x) x^n
5). f(x)=cx^n
6). f(x)=π
7). f(x)=6x^-3
8). f(x)=√x
9). f(x)=2x+5
10). f(x)=2+√x

Vocaloid · Answer

I will not do the whole thing for you, but I will help you get started

The main differentiation rule you'll be using is the power rule:

$$\frac{ d }{ dx }x^{n}=n*x^{n-1}$$
Thinking about this in layman's terms, you take the exponent, bring it down to the front, and reduce the original exponent by 1

If there is no variable (a.k.a it's a constant) the derivative is 0.

I'll do both a) and b) as examples to get you started

a) f(x) = 3 is a constant, so the derivative is 0
b) f(x) = 8x². keep the coefficient 8. focus on the x^2 part. bringing the exponent down in front gives us

8 * 2 * x^(2)

Now, we reduce the exponent by 1

Final result: 8 * 2 * x^1, or 16x

If you'd like to give the other ones a try, I'd be happy to help if you get stuck or want to check your answer