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Derivative of y=(x-1)²(x+2)
Derivative of (3t^3-4t+6)^3
Derivative of y=2*e^x+cos(3*x)
Derivative of sqrt(1-2x)
Identical expressions
(three t^ three -4t+ six)^3
(3t cubed minus 4t plus 6) cubed
(three t to the power of three minus 4t plus six) cubed
(3t3-4t+6)3
3t3-4t+63
(3t³-4t+6)³
(3t to the power of 3-4t+6) to the power of 3
3t^3-4t+6^3
Similar expressions
(3t^3-4t-6)^3
(3t^3+4t+6)^3

The derivative of the function/ (3t^3-4t+6)^3

Derivative of (3t^3-4t+6)^3

The solution

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                3
/   3          \ 
\3*t  - 4*t + 6/

$$\left(3 t^{3} - 4 t + 6\right)^{3}$$

  /                3\
d |/   3          \ |
--\\3*t  - 4*t + 6/ /
dt

$$\frac{d}{d t} \left(3 t^{3} - 4 t + 6\right)^{3}$$

Transform

Detail solution

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

$3 \cdot \left(9 t^{2} - 4\right) \left(3 t^{3} - 4 t + 6\right)^{2}$
Now simplify:

$\left(27 t^{2} - 12\right) \left(3 t^{3} - 4 t + 6\right)^{2}$

The answer is:

$\left(27 t^{2} - 12\right) \left(3 t^{3} - 4 t + 6\right)^{2}$

The graph

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The first derivative [src]

                2              
/   3          \  /          2\
\3*t  - 4*t + 6/ *\-12 + 27*t /

$$\left(27 t^{2} - 12\right) \left(3 t^{3} - 4 t + 6\right)^{2}$$

Simplify

The second derivative [src]

  /           2                       \                 
  |/        2\        /             3\| /             3\
6*\\-4 + 9*t /  + 9*t*\6 - 4*t + 3*t //*\6 - 4*t + 3*t /

$$6 \cdot \left(9 t \left(3 t^{3} - 4 t + 6\right) + \left(9 t^{2} - 4\right)^{2}\right) \left(3 t^{3} - 4 t + 6\right)$$

Simplify

The third derivative [src]

  /           3                     2                                    \
  |/        2\      /             3\         /        2\ /             3\|
6*\\-4 + 9*t /  + 9*\6 - 4*t + 3*t /  + 54*t*\-4 + 9*t /*\6 - 4*t + 3*t //

$$6 \cdot \left(54 t \left(9 t^{2} - 4\right) \left(3 t^{3} - 4 t + 6\right) + \left(9 t^{2} - 4\right)^{3} + 9 \left(3 t^{3} - 4 t + 6\right)^{2}\right)$$

Simplify

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Derivative of (3t^3-4t+6)^3

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The solution