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Identical expressions
four /(nine +7x)^ five
4 divide by (9 plus 7x) to the power of 5
four divide by (nine plus 7x) to the power of five
4/(9+7x)5
4/9+7x5
4/(9+7x)⁵
4/9+7x^5
4 divide by (9+7x)^5
Similar expressions
4/(9-7x)^5

The derivative of the function/ 4/(9+7x)^5

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

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) /

$$\frac{d}{d x} \frac{4}{\left(7 x + 9\right)^{5}}$$

Transform

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = \left(7 x + 9\right)^{5}$ .
2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(7 x + 9\right)^{5}$ :
  1. Let $u = 7 x + 9$ .
  2. Apply the power rule: $u^{5}$ goes to $5 u^{4}$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(7 x + 9\right)$ :
    1. Differentiate $7 x + 9$ term by term:
      1. The derivative of the constant $9$ is zero.
      2. The derivative of a constant times a function is the constant times the derivative of the function.
        
        Apply the power rule: $x$ goes to $1$
        
        So, the result is: $7$
      The result is: $7$
    The result of the chain rule is:
    
    $35 \left(7 x + 9\right)^{4}$
  The result of the chain rule is:
  
  $- \frac{35}{\left(7 x + 9\right)^{6}}$
So, the result is: $- \frac{140}{\left(7 x + 9\right)^{6}}$

The answer is:

$- \frac{140}{\left(7 x + 9\right)^{6}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  -140    
----------
         6
(9 + 7*x)

$$- \frac{140}{\left(7 x + 9\right)^{6}}$$

Simplify

The second derivative [src]

   5880   
----------
         7
(9 + 7*x)

$$\frac{5880}{\left(7 x + 9\right)^{7}}$$

Simplify

The third derivative [src]

 -288120  
----------
         8
(9 + 7*x)

$$- \frac{288120}{\left(7 x + 9\right)^{8}}$$

Simplify

The graph

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