To find the gradient/slope, we need to first choose two points on the line. You can choose any two points you like, as long as they are on the line you are trying to find the slope of.

Point 1 = (2,2)

Point 2 = (5,8)

Now, we can plug in these points to the formula and solve.

(8 - 2) / (5 - 2)

6 / 3

The gradient of the blue line is 2.

Hope this helps!! :)

7 0

3 years ago

Find the derivative of the image below

Nata [24]

$~~~\dfrac{d}{dx} f(x) \\ \\=\dfrac{d}{dx} \left(x^3 \cdot \log_6 x \right)\\\\=x^3\dfrac{d}{dx} \left(\log_6 x\right) + \log_6 (x)\dfrac d{dx} x^3 \\\\=x^3 \cdot \dfrac 1{x \ln 6} + \log _6 (x) \cdot 3x^2\\\\=\dfrac{x^2}{\ln 6} + \log_6(x) \cdot 3x^2\\\\\\=x^2 \left(\dfrac 1{\ln 6} + 3\log_6 x \right)$

$\text{The derivative is now in a form of}~ x^A (B + C \log_D (x))$

3 0

2 years ago