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Derivative of:
Derivative of e^(6*x)
Derivative of -1/y
Derivative of sin^2(x^2)
Derivative of log(1+1/(x^2))
Identical expressions
-((three)/(three *x+ seven))
minus ((3) divide by (3 multiply by x plus 7))
minus ((three) divide by (three multiply by x plus seven))
-((3)/(3x+7))
-3/3x+7
-((3) divide by (3*x+7))
Similar expressions
-((3)/(3*x-7))
((3)/(3*x+7))

The derivative of the function/ -((3)/(3*x+7))

Derivative of -((3)/(3*x+7))

The solution

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  -3   
-------
3*x + 7

$$- \frac{3}{3 x + 7}$$

-3/(3*x + 7)

Detail solution

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

$\frac{9}{\left(3 x + 7\right)^{2}}$

The answer is:

$\frac{9}{\left(3 x + 7\right)^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    9     
----------
         2
(3*x + 7)

$$\frac{9}{\left(3 x + 7\right)^{2}}$$

Simplify

The second derivative [src]

   -54    
----------
         3
(7 + 3*x)

$$- \frac{54}{\left(3 x + 7\right)^{3}}$$

Simplify

The third derivative [src]

   486    
----------
         4
(7 + 3*x)

$$\frac{486}{\left(3 x + 7\right)^{4}}$$

Simplify