Given: f(x) = 6x² + 3x
Derivative: f'(x) = 12x + 3
f'(1) = 12*1 + 3 = 15
Answer: 15

Given: 4x³ dx
Integrate: 4x³ dx = 4 * x / 4
Result = x
Answer: x

Given: matrix = [[1,2],[3,5]]
determinant = (1*5) - (2*3) = 5 - 6
determinant = -1
Answer: -1

Given: 4x + 2y = 10, x + y = 3
From x + y = 3 y = 3 - x
Substitute: 4x + 2(3 - x) = 10 4x + 6 - 2x = 10 2x = 4 x = 2
y = 3 - 2 = 1
Answer: x = 2, y = 1

Given: dy/dx = x, y(0) = 1
Integrate: y = x dx = 0.5x² + C
Use y(0)=1 1 = 0.5*0² + C C = 1
y(3) = 0.5*3² + 1 = 4.5 + 1
y(3) = 5.5
Answer: 5.5