differentiate?

Question

h(x) = -8cscx + e^(x)cotx


rly need help

Answer 1

The first term is just one function, where the second term is a product of functions. So, we will have to use the product rule on the second term.

d/dx(csc x) = -csc x cot x

d/dx (cot x) = -csc² x

d/dx e^x = e^x

The product rule tells us to take function 1 times the derivative of function 2 and then add function 2 times the derivative of function 1. A useful mnemonic device for the rule is 1 dee 2 plus 2 dee 1.

h'(x) = -8(-csc x cot x) + e^x(-csc² x) + cot x (e^x)

Simplify to get h'(x) = 8csc x cot x - e^xcsc²x + e^x cot x

Answer 2

h(x) = -8/sin(x) +e^x/tan x
h´(x) = 8*cos(x)/sin^2(x) +1/tan^2(x) *((e^x*tan(x)-e^(x)/cos^2(x)))
I think e^(x)cotx means e^x *(cot x) so cot (x) is NOT in the exponent