Question

http://prntscr.com/kjaelo

Answer 1

@Shadow

Answer 2

a) y = cosh(3x)

the derivative of cosh works almost the same way as the derivative of cos, except you would get sinh as the derivative instead of cosh

apply the chain rule to the 3x part as usual

Answer 3

b) r = sinh(2t^2 -1)

the derivative of sinh is cosh, apply the chain rule again to the 2t^2 - 1 part

Answer 4

c) apply the product rule

g(x) = (x-1)^3 * sech^2(x)

g'(x) = 3(x-1)^2 * sech^2(x) + (x-1)^3*2 * (d/dx) of sech(x)

the derivative of sech(x) is -sech^2(x) * tanh(x) so plug this back into the d/dx of sech(x) part

then after that it's just factoring/algebraic simplification

Answer 5

d) to take the derivative of tanh(ln(x)) consider the derivative tanh(x) = sech^2(x)

so the derivative of tanh(ln(x)) would just be the sech^2(ln(x)) * the derivative of ln(x) according to the chain rule

Answer 6

Thank you @Komaeda !