Question

x=a(3costheta+cos3theta) find the second order derivative

Answer 1

Answer :

(d²y / dx²) = (-6a cos Φ )

Step-by-step explanation:

x = a(3cosΦ+cos3Φ)

Differentiation wrt Φ

(dx / dΦ) = a x d/dΦ(3cosΦ+cos3Φ)

= a ( 3 (-sin Φ )+( -sinΦ) x (d/dx(3Φ))

= a (3 (- sinΦ ) + ( - sinΦ ) x (3))

= a (- 3sinΦ - 3sinΦ )

= a (-3) (sinΦ + sinΦ )

= -3a (2 sin Φ)

(dx /dΦ)= -6a (sinΦ)

again differentiate wrt Φ

(d²x / dΦ²) = d/dx( -6a (sinΦ ) )

=( -6a (d /dx (sinΦ))

= (-6a ( cos Φ))

= (-6a cosΦ )

(d²x / dΦ²) = (-6a cos Φ )