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

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

Function f() - derivative -N order at the point
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The solution

You have entered [src] 
                3
/   3          \ 
\3*t  - 4*t + 6/
(3t3−4t+6)3\left(3 t^{3} - 4 t + 6\right)^{3} 
  /                3\
d |/   3          \ |
--\\3*t  - 4*t + 6/ /
dt
ddt(3t3−4t+6)3\frac{d}{d t} \left(3 t^{3} - 4 t + 6\right)^{3}
Transform
Detail solution

  1. Let u=3t3−4t+6u = 3 t^{3} - 4 t + 6.

  2. Apply the power rule: u3u^{3} goes to 3u23 u^{2}

  3. Then, apply the chain rule. Multiply by ddt(3t3−4t+6)\frac{d}{d t} \left(3 t^{3} - 4 t + 6\right):

    1. Differentiate 3t3−4t+63 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: t3t^{3} goes to 3t23 t^{2}

        So, the result is: 9t29 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: tt goes to 11

          So, the result is: 44

        So, the result is: −4-4

      3. The derivative of the constant 66 is zero.

      The result is: 9t2−49 t^{2} - 4

    The result of the chain rule is:

    3⋅(9t2−4)(3t3−4t+6)23 \cdot \left(9 t^{2} - 4\right) \left(3 t^{3} - 4 t + 6\right)^{2}

  4. Now simplify:

    (27t2−12)(3t3−4t+6)2\left(27 t^{2} - 12\right) \left(3 t^{3} - 4 t + 6\right)^{2}

The answer is:

(27t2−12)(3t3−4t+6)2\left(27 t^{2} - 12\right) \left(3 t^{3} - 4 t + 6\right)^{2}

The graph
02468-8-6-4-2-1010-5000000000050000000000
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The first derivative [src] 
                2              
/   3          \  /          2\
\3*t  - 4*t + 6/ *\-12 + 27*t /
(27t2−12)(3t3−4t+6)2\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⋅(9t(3t3−4t+6)+(9t2−4)2)(3t3−4t+6)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⋅(54t(9t2−4)(3t3−4t+6)+(9t2−4)3+9(3t3−4t+6)2)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
The graph
Derivative of (3t^3-4t+6)^3
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