What is the second derivative of sin(7x + 2)?

Answer 1

f(x)=sin(7x + 2)
f'(x)=7cos(7x + 2) <-- chain rule
f''(x)=7(-7sin(7x+2)) <-- chain rule again
f''(x)=-49sin(7x+2)

Answer 2

This is a composite function, so the first derivative is

7cos(7x + 2), then you must take the second derivative, which will be
- 49sin(7x+2)

(The dash is showing the 49 is negative)

Answer 3

y = sin(7x + 2)

let u = 7x + 2
d/du sin(u) = cos(u)
d/dx (7x + 2) = 7

y' = 7cos(7x + 2) <== first derivative

y'' = 7 d/dx cos(7x + 2)

chian rule again:
let u = 7x + 2
then d/du cos(u) = -sin(u)
d/dx (7x + 2) = 7

y'' = 7 * 7 * -sin(7x + 2)

y'' = -49sin(7x+2) <== second derivative


Rec