## sandra 4 years ago Can someone help me with basic derivatives: 3x^2 + 5x + 5?

1. Ana2

6x + 5

2. A_clan

3(2X) + 5

3. clauixx

6x+5

4. Ana2

The rules are: derivative of x^n = n * x^(n-1) derivative of sum is the sum of the derivatives. derivative of a constant times a function equals the constant times the derivative of the function.

The approach is pretty straightforward -- $$x^2$$ on its own derives to 2x. Since it has a 3 in front of it, we get 3(2x), as above. x derives to $$x^0$$, which is the same as 1. Since it has a 5 in front of it, we get 5, as above. 5 disappears, because it is a constant and the derivative of a constant is 0.

6. Ana2

So d/dx (3x^2 +5x + 5) = d/dx (3x^2) + d/dx (5x) + d/dx (5) = 3* d/dx (x^2) + 5 * d/dx (x) + 0 = 3 * 2 x + 5 * 1 = 6x + 5

7. amistre64

$\lim_{h\rightarrow 0}\ \frac{f(x+h)-f(x)}{h}$ $(3(x+h)^2 +5(x+h) +5)-(3x^2 +5x +5)//h$ $(3(x^2+2xh+h^2) +5x+5h +5 -3x^2 -5x -5)//h$ $3x^2+6xh+3h^2 +5x+5h +5 -3x^2 -5x -5)//h$ $\frac{6xh+3h^2+5h}{h}$ $\lim_{h\rightarrow0}\ 6x+3h+5\ =\ 6x+5$

8. amistre64

the long version lets you appreciate the shortcut rules ;)