Hi there!

can i get some with #2 and #6 calculus? show your work.

!

1.  36 -24x

2.  -6x/ (3x^2+5)^2

Step-by-step explanation:

2.

y = 1 - 3u^2

dy/dx = -6u du/dx

We can find du/dx

u = 3 -2x

du/dx = -2

Substituting back in for  u and du/dx

dy/dx = -6u du/dx

dy/dx = -6 (3-2x) (-2)

dy/dx = 12 (3-2x)

         = 36 -24x

6.  y = 1/u = u ^ -1

dy/dx = -1 u^-2 du/dx

u = 3x^2 +5

du/dx = 6x

Substituting back in for  u and du/dx

dy/dx = - (3x^2+5) ^-2 (6x)

         = -6x/ (3x^2+5)^2

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!