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(3x^5-2)^4
The derivative of the function/ (3x^5-2)^4

Derivative of (3x^5-2)^4

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
          4
/   5    \ 
\3*x  - 2/
$$\left(3 x^{5} - 2\right)^{4}$$ 
  /          4\
d |/   5    \ |
--\\3*x  - 2/ /
dx
$$\frac{d}{d x} \left(3 x^{5} - 2\right)^{4}$$
Transform
Detail solution

  1. Let .

  2. Apply the power rule: goes to

  3. Then, apply the chain rule. Multiply by :

    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 the constant is zero.

      The result is:

    The result of the chain rule is:

  4. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
                3
    4 /   5    \ 
60*x *\3*x  - 2/
$$60 x^{4} \left(3 x^{5} - 2\right)^{3}$$
Simplify
The second derivative [src] 
                 2             
    3 /        5\  /         5\
60*x *\-2 + 3*x / *\-8 + 57*x /
$$60 x^{3} \left(3 x^{5} - 2\right)^{2} \cdot \left(57 x^{5} - 8\right)$$
Simplify
The third derivative [src] 
                   /             2                              \
     2 /        5\ |  /        5\         10       5 /        5\|
360*x *\-2 + 3*x /*\2*\-2 + 3*x /  + 225*x   + 90*x *\-2 + 3*x //
$$360 x^{2} \cdot \left(3 x^{5} - 2\right) \left(225 x^{10} + 90 x^{5} \cdot \left(3 x^{5} - 2\right) + 2 \left(3 x^{5} - 2\right)^{2}\right)$$
Simplify
The graph
Derivative of (3x^5-2)^4
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