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Identical expressions
(7x^ two -5x+ nine)^ six
(7x squared minus 5x plus 9) to the power of 6
(7x to the power of two minus 5x plus nine) to the power of six
(7x2-5x+9)6
7x2-5x+96
(7x²-5x+9)⁶
(7x to the power of 2-5x+9) to the power of 6
7x^2-5x+9^6
Similar expressions
(7x^2+5x+9)^6
(7x^2-5x-9)^6

The derivative of the function/ (7x^2-5x+9)^6

Derivative of (7x^2-5x+9)^6

The solution

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                6
/   2          \ 
\7*x  - 5*x + 9/

$$\left(7 x^{2} - 5 x + 9\right)^{6}$$

  /                6\
d |/   2          \ |
--\\7*x  - 5*x + 9/ /
dx

$$\frac{d}{d x} \left(7 x^{2} - 5 x + 9\right)^{6}$$

Transform

Detail solution

Let $u = 7 x^{2} - 5 x + 9$ .
Apply the power rule: $u^{6}$ goes to $6 u^{5}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(7 x^{2} - 5 x + 9\right)$ :
1. Differentiate $7 x^{2} - 5 x + 9$ 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: $x^{2}$ goes to $2 x$
    So, the result is: $14 x$
  2. The derivative of a constant times a function is the constant times the derivative of the function.
    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: $5$
    So, the result is: $-5$
  3. The derivative of the constant $9$ is zero.
  The result is: $14 x - 5$
The result of the chain rule is:

$6 \cdot \left(14 x - 5\right) \left(7 x^{2} - 5 x + 9\right)^{5}$
Now simplify:

$\left(84 x - 30\right) \left(7 x^{2} - 5 x + 9\right)^{5}$

The answer is:

$\left(84 x - 30\right) \left(7 x^{2} - 5 x + 9\right)^{5}$

The graph

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The first derivative [src]

                5             
/   2          \              
\7*x  - 5*x + 9/ *(-30 + 84*x)

$$\left(84 x - 30\right) \left(7 x^{2} - 5 x + 9\right)^{5}$$

Simplify

The second derivative [src]

                  4                                      
  /             2\  /                          2       2\
6*\9 - 5*x + 7*x / *\126 - 70*x + 5*(-5 + 14*x)  + 98*x /

$$6 \left(7 x^{2} - 5 x + 9\right)^{4} \cdot \left(98 x^{2} - 70 x + 5 \left(14 x - 5\right)^{2} + 126\right)$$

Simplify

The third derivative [src]

                   3                                                    
   /             2\              /                           2        2\
60*\9 - 5*x + 7*x / *(-5 + 14*x)*\189 - 105*x + 2*(-5 + 14*x)  + 147*x /

$$60 \cdot \left(14 x - 5\right) \left(7 x^{2} - 5 x + 9\right)^{3} \cdot \left(147 x^{2} - 105 x + 2 \left(14 x - 5\right)^{2} + 189\right)$$

Simplify

The graph

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Derivative of (7x^2-5x+9)^6

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