Considering f(x) = (2 - 5x)³, find f'(x)

Let’s re-write the function as follows:

y = (-5x + 2)3

Let's consider the function

u  = -5x + 2
u' = -5

We know that the derivative of uⁿ, f'(u) = nu^n-1du/dx. Therefore:

un    = (-5x + 2)3
(un)' = nun-1u'
      = 3(-5x + 2)2(-5)
      = -15(-5x + 2)2

y = (-2x3 + 7)-4

u  = -2x3 + 7
u' = -6x2

f  = u-4

un    = (-2x3 + 7)-4
(un)' = nun-1u'
      = -4(-2x3 + 7)-5(-6x2)
      = -24x2(7 - 2x3)-5

Find the derivative of

Let's consider

u  = 4x - 7

u' = 4

Remember the formula to find the derivative of the inverse of a function:

f'(x) =

Find the derivative of

Let's consider

u  = x - 1

u' = 1

And let's consider

v  = x + 1

v' = 1

Remember the formula to find the derivative of the division of two functions:

Considering f(x) =

find f'(x)

Let’s re-write the function as follows:

y = (2x + 1)-3

Let's consider the function

u  = 2x + 1
u' = 2

We know that the derivative of uⁿ, f'(u) = nu^n-1du/dx. Therefore:

un    = (2x + 1)-3
(un)' = nun-1u'
      = -3(2x + 1)-4(2)
      = -6(2x + 1)-4

       =