Core Pure - Differentiation

Question 1

d/dx( sinh(x) )

Answer 1

cosh(x)

Question 2

d/dx( cosh(x) )

Answer 2

sinh(x)

Question 3

d/dx( tanh(x) )

Answer 3

sech²(x)

Question 4

d/dx( cosech(x) )

Answer 4

-coth(x) cosech(x)

Question 4

d/dx( sech(x) )

Answer 4

-tanh(x) sech(x)

IMPORTANT - DIFFERENT TO NORMAL TRIG AS THERE IS A MINUS SIGN

Question 5

d/dx( coth(x) )

Answer 5

-cosech²(x)

Question 6

What is the most important thing to remember when differentiating hyperbolic functions?

Answer 6

For all but ONE of the standard 6 hyperbolic functions, they differentiate the same as normal trigonometric functions. When differentiating sech(x), it becomes - tanh(x) sech(x), in normal trig it is positive but for hyperbolics it is negative

DO NOT FORGET THE MINUS