Question

Find d²y/dx², when:

(i) y = x³ + tan x

(ii) y = x² + 3x + 2

(iii) y = x cos x

(iv) y = 2 sin x + 3 cos x

(v) y = e^-x cos x

(vi) y = a sin x – b cos x

Answer 1

(i) y = x³ + tan x

Diff. w.r.t. x on both

dy/dx = d/dx(x³ + tanx) 

= 3x² + sec²x

Again diff. w.r.t. x on both sides

(ii) y = x² + 3x + 2

Diff. w.r.t. x on both sides,

(iii) y = x cos x

Diff. w.r.t. x on both sides,

(iv) y = 2 sin x + 3 cos x

Diff. w.r.t. x on both sides,

(v) y = e^-ex cos x

Diff. w.r.t. x on both sides,

(vi) y = a sin x – b cos x

Diff. w.r.t. x on both sides,