Question

If y = 3sinx + 4cosx find d²y / dx²​

Answer 1

Step-by-step explanation:

We have,

$y = 3 \sin(x) + 4 \cos(x)$

Differentiating both sides w.r.t x,

$\frac{dy}{dx} = 3 \cos(x) - 4 \sin(x)$

Again differentiating both sides w.r.t x, we have,

$\frac{ {d}^{2}y }{d {x}^{2} } = - 3 \sin(x) - 4 \cos(x)$

$\implies \frac{ {d}^{2} y}{d {x}^{2} } = - (3 \sin(x) + 4 \cos(x) )$

$\implies \frac{ {d}^{2}y }{d {x}^{2} } = - y$