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4/(9+7x)^5

Derivative of 4/(9+7x)^5

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
    4     
----------
         5
(9 + 7*x) 
$$\frac{4}{\left(7 x + 9\right)^{5}}$$
d /    4     \
--|----------|
dx|         5|
  \(9 + 7*x) /
$$\frac{d}{d x} \frac{4}{\left(7 x + 9\right)^{5}}$$
Detail solution
  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. Let .

    2. Apply the power rule: goes to

    3. Then, apply the chain rule. Multiply by :

      1. Let .

      2. Apply the power rule: goes to

      3. Then, apply the chain rule. Multiply by :

        1. Differentiate term by term:

          1. The derivative of the constant is zero.

          2. The derivative of a constant times a function is the constant times the derivative of the function.

            1. Apply the power rule: goes to

            So, the result is:

          The result is:

        The result of the chain rule is:

      The result of the chain rule is:

    So, the result is:


The answer is:

The graph
The first derivative [src]
  -140    
----------
         6
(9 + 7*x) 
$$- \frac{140}{\left(7 x + 9\right)^{6}}$$
The second derivative [src]
   5880   
----------
         7
(9 + 7*x) 
$$\frac{5880}{\left(7 x + 9\right)^{7}}$$
The third derivative [src]
 -288120  
----------
         8
(9 + 7*x) 
$$- \frac{288120}{\left(7 x + 9\right)^{8}}$$
The graph
Derivative of 4/(9+7x)^5