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

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

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

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The solution

You have entered [src] 
                6
/   2          \ 
\7*x  - 5*x + 9/
(7x2−5x+9)6\left(7 x^{2} - 5 x + 9\right)^{6} 
  /                6\
d |/   2          \ |
--\\7*x  - 5*x + 9/ /
dx
ddx(7x2−5x+9)6\frac{d}{d x} \left(7 x^{2} - 5 x + 9\right)^{6}
Transform
Detail solution

  1. Let u=7x2−5x+9u = 7 x^{2} - 5 x + 9.

  2. Apply the power rule: u6u^{6} goes to 6u56 u^{5}

  3. Then, apply the chain rule. Multiply by ddx(7x2−5x+9)\frac{d}{d x} \left(7 x^{2} - 5 x + 9\right):

    1. Differentiate 7x2−5x+97 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: x2x^{2} goes to 2x2 x

        So, the result is: 14x14 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: xx goes to 11

          So, the result is: 55

        So, the result is: −5-5

      3. The derivative of the constant 99 is zero.

      The result is: 14x−514 x - 5

    The result of the chain rule is:

    6⋅(14x−5)(7x2−5x+9)56 \cdot \left(14 x - 5\right) \left(7 x^{2} - 5 x + 9\right)^{5}

  4. Now simplify:

    (84x−30)(7x2−5x+9)5\left(84 x - 30\right) \left(7 x^{2} - 5 x + 9\right)^{5}

The answer is:

(84x−30)(7x2−5x+9)5\left(84 x - 30\right) \left(7 x^{2} - 5 x + 9\right)^{5}

The graph
02468-8-6-4-2-1010-500000000000000000500000000000000000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
                5             
/   2          \              
\7*x  - 5*x + 9/ *(-30 + 84*x)
(84x−30)(7x2−5x+9)5\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(7x2−5x+9)4⋅(98x2−70x+5(14x−5)2+126)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⋅(14x−5)(7x2−5x+9)3⋅(147x2−105x+2(14x−5)2+189)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
Derivative of (7x^2-5x+9)^6
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