Find the gradient of 4(8x+2)^4 at X coordinate 2

To find a gradient at a given point, first we differentiate then we sub in the x coordinate of the point. To differentiate 4(8x+2)⁴ we must use the chain rule. First we let u= 8x+2 and differentiate this to find du/dx = 8. Then we must find the rest, we differentiate y = 4u⁴ , dy/du = 16u³ . The chain rule then states that dy/dx = dy/du x du/dx so we get 16u³ x 8 and as u = 8x+2 we get: 128(8x+2)³.To find the value at X coordinate 2 we sub the value into dy/dx and get 128(8(2)+2)³ multiply this out and we get 128 x 18³ = 746,946. So the gradient of 4(8x+2)⁴ at X coordinate 2 is 746,946.