Differentiate the following functions w.r.t x.:-
1.(2x+3)(x³-x+2)
2.sin²(3x-2)
For 1. use the product rule. d(uv)/dx = u.dv/dx + v.du/dx, where u = (2x+3) and v = (x³-x+2)
d(uv)/dx = (2x+3)(3x^2 -1) + (x³-x+2)(2)
For 2. use the chain rule. df(x)/dx = d(f(u))/du.du/dx, where f(x) = sin²(3x-2) and f(u) = sin²(u), with u = 3x - 2
f(u) = sin²(u), giving df/du = 2sin(u).cos(u) = sin(2u)
u = 3x - 2 giving du/dx = 3
Then, df(x)/dx = d(f(u))/du.du/dx = sin(2u).3
df/dx = 3sin(2(3x-2))