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  • Derivative of:
  • Derivative of (-2)/x^3 Derivative of (-2)/x^3
  • Derivative of 1/3*x^3-4*x Derivative of 1/3*x^3-4*x
  • Derivative of f(x)=2x-3 Derivative of f(x)=2x-3
  • Derivative of y=x(x-1) Derivative of y=x(x-1)

  • Identical expressions

  • pi*r*(four *t^ two - two *t^ three)/ two
  • Pi multiply by r multiply by (4 multiply by t squared minus 2 multiply by t cubed ) divide by 2
  • Pi multiply by r multiply by (four multiply by t to the power of two minus two multiply by t to the power of three) divide by two
  • pi*r*(4*t2-2*t3)/2
  • pi*r*4*t2-2*t3/2
  • pi*r*(4*t²-2*t³)/2
  • pi*r*(4*t to the power of 2-2*t to the power of 3)/2
  • pir(4t^2-2t^3)/2
  • pir(4t2-2t3)/2
  • pir4t2-2t3/2
  • pir4t^2-2t^3/2
  • pi*r*(4*t^2-2*t^3) divide by 2

  • Similar expressions

  • pi*r*(4*t^2+2*t^3)/2
The derivative of the function/ pi*r*(4*t^2-2*t^3)/2

Derivative of pi*r*(4*t^2-2*t^3)/2

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
     /   2      3\
pi*r*\4*t  - 2*t /
------------------
        2
$$\frac{\pi r \left(- 2 t^{3} + 4 t^{2}\right)}{2}$$ 
((pi*r)*(4*t^2 - 2*t^3))/2
Detail solution

  1. 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. Differentiate 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: goes to

          So, the result is:

        2. The derivative of a constant times a function is the constant times the derivative of the function.

          1. Apply the power rule: goes to

          So, the result is:

        The result is:

      So, the result is:

    So, the result is:

  2. Now simplify:

The answer is:

The first derivative [src] 
     /     2      \
pi*r*\- 6*t  + 8*t/
-------------------
         2
$$\frac{\pi r \left(- 6 t^{2} + 8 t\right)}{2}$$
Simplify
The second derivative [src] 
-2*pi*r*(-2 + 3*t)
$$- 2 \pi r \left(3 t - 2\right)$$
Simplify
The third derivative [src] 
-6*pi*r
$$- 6 \pi r$$
Simplify
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