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Identical expressions
(two -7x^ two + three x)^3
(2 minus 7x squared plus 3x) cubed
(two minus 7x to the power of two plus three x) cubed
(2-7x2+3x)3
2-7x2+3x3
(2-7x²+3x)³
(2-7x to the power of 2+3x) to the power of 3
2-7x^2+3x^3
Similar expressions
(2-7x^2-3x)^3
(2+7x^2+3x)^3

The derivative of the function/ (2-7x^2+3x)^3

Derivative of (2-7x^2+3x)^3

The solution

You have entered [src]

                3
/       2      \ 
\2 - 7*x  + 3*x/

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

  /                3\
d |/       2      \ |
--\\2 - 7*x  + 3*x/ /
dx

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

Transform

Detail solution

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

$3 \cdot \left(3 - 14 x\right) \left(- 7 x^{2} + 3 x + 2\right)^{2}$
Now simplify:

$\left(9 - 42 x\right) \left(- 7 x^{2} + 3 x + 2\right)^{2}$

The answer is:

$\left(9 - 42 x\right) \left(- 7 x^{2} + 3 x + 2\right)^{2}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

                2           
/       2      \            
\2 - 7*x  + 3*x/ *(9 - 42*x)

$$\left(- 42 x + 9\right) \left(- 7 x^{2} + 3 x + 2\right)^{2}$$

Simplify

The second derivative [src]

  /       2      \ /                 2              2\
6*\2 - 7*x  + 3*x/*\-14 + (-3 + 14*x)  - 21*x + 49*x /

$$6 \left(- 7 x^{2} + 3 x + 2\right) \left(49 x^{2} + \left(14 x - 3\right)^{2} - 21 x - 14\right)$$

Simplify

The third derivative [src]

              /                2        2        \
6*(-3 + 14*x)*\84 - (-3 + 14*x)  - 294*x  + 126*x/

$$6 \cdot \left(14 x - 3\right) \left(- 294 x^{2} - \left(14 x - 3\right)^{2} + 126 x + 84\right)$$

Simplify

The graph

Derivative of (2-7x^2+3x)^3