# Thread: differentiontion of hyperbolic trigonometry function

1. ## differentiontion of hyperbolic trigonometry function

is it use same method to do differentiation between hyperbolic trigo and normaal trigo?

if the question ask d/dx(4sinh^5 3x) after i differentiate it, is the answer become 60 sinh^4 3x?

2. Originally Posted by emperror123
is it use same method to do differentiation between hyperbolic trigo and normaal trigo?

if the question ask d/dx(4sinh^5 3x) after i differentiate it, is the answer become 60 sinh^4 3x?
I suspect your text book will tell you that the derivative of sin(x) is cos(x), the derivative of cos(x) is -sin(x), the derivative of sinh(x) is cosh(x), and the derivative of cosh(x) is sinh(x).
No, the derivative of $4 sinh^5(3x)$ is NOT $60 sinh^4(3x)$. Nor is the derivative of $4 sin^5(3x)$ equal to $60 sin^4(3x)$.

The derivative of $4sin^5(3x)$ is $4(5)(sin^4(3x)$ times the derivative of $sin(3x)$ which is $3 cos(3x)$. That is, the derivative of $4sin^5(3x)$ is $60sin^4(3x)cos(3x)$.

Now, back to you- what is the derivative of $4 sinh^5(3x)$? What is the derivative of $4 cosh^5(3x)$?

3. derivation of 4 sinh^5 3x = 60sinh^4 3x cosh 3x
derivation of 4 cosh^5 3x = 60 cosh^4 3x sinh 3x