problem with the chain rule

subzero12 wrote: »

hey guys im im just wondering could anyone help me with these
two problems using the chain rule,

question one is

sin(3e^x-2cosx+10e^x+2sinhx)

and question 2 is

cos(3lnx-2sinhx+2e^x-4tanx)

thanks in advance for anyhelp

another question if i have 2lnx is that the same as 2/x?

For the chain rule you have two functions in it. For example for the first question the sin() is a function and whats in the brackets is another function. Differentiate them both and muliply

1. sin(3e^x-2cosx+10e^x+2sinhx)

Differentiate sin to get cos, Differentiate the stuff in the brackets to get 3e^x-2cosx+10e^x+2coshx (just diff each component in brcket). This is then muliplied out the front to get:

(3e^x+2sinx+10e^x+2coshx)cos(3e^x-2cosx+10e^x+2sinhx)

2. cos(3lnx-2sinhx+2e^x-4tanx)

Differentiate cos to get -sin, Differentiate the stuff in the brackets to get (3/x)-2coshx+2e^x-4sec^2(x) (just diff each component in brcket). This is then muliplied out the front to get:

[(3/x)-2coshx+2e^x-4sec^2(x)]*-sin(3lnx-2sinhx+2e^x-4tanx)

3. THe differentiation of 2lnx is 2/x



Does that help you?