Possible derivation:
d/dy(1.5-4 y-2 y^2+cos((pi t)/12))
Differentiate the sum term by term and factor out constants:
= d/dy(1.5)-4 (d/dy(y))-2 (d/dy(y^2))+d/dy(cos((pi t)/12))
The derivative of 1.5 is zero:
= -4 (d/dy(y))-2 (d/dy(y^2))+d/dy(cos((pi t)/12))+0
Simplify the expression:
= -4 (d/dy(y))-2 (d/dy(y^2))+d/dy(cos((pi t)/12))
The derivative of y is 1:
= -2 (d/dy(y^2))+d/dy(cos((pi t)/12))-1 4
Use the power rule, d/dy(y^n) = n y^(n-1), where n = 2: d/dy(y^2) = 2 y:
= -4+d/dy(cos((pi t)/12))-2 2 y
Simplify the expression:
= -4-4 y+d/dy(cos((pi t)/12))
The derivative of cos((pi t)/12) is zero:
= -4-4 y+0
Simplify the expression:
Answer: | = -4-4y
