derivatives problem

Question

h(x)= xcosh(x² -4), then h^'' (2)=?

Answer 1

first you want to find h ' (x)

h ' (x) = cosh(x^2 - 4) + 2x^2*sinh(x^2 - 4)

then you can find h '' (x)

h '' (x) = 6x sinh(x^2 - 4) + 4x^3 * cosh(x^2 - 4)

then plug in x = 2

h '' (2) = 6(2) sinh(2^2 - 4) + 4(2)^3 * cosh(2^2 - 4)

h '' (2) = 12 sinh(4 - 4) + 4(8)cosh(4 - 4)

h '' (2) = 12 sinh(0) + 32 cosh(0)

h '' (2) = 12(0) + 32(1) = 32

so the end value for this scenario should be h '' (2) = 32