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y=(x²+3x)⁴
The derivative of the function/ y=(x²+3x)⁴

Derivative of y=(x²+3x)⁴

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
          4
/ 2      \ 
\x  + 3*x/
$$\left(x^{2} + 3 x\right)^{4}$$ 
  /          4\
d |/ 2      \ |
--\\x  + 3*x/ /
dx
$$\frac{d}{d x} \left(x^{2} + 3 x\right)^{4}$$
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. Apply the power rule: goes to

      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:

    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           
/ 2      \            
\x  + 3*x/ *(12 + 8*x)
$$\left(8 x + 12\right) \left(x^{2} + 3 x\right)^{3}$$
Simplify
The second derivative [src] 
   2        2 /           2              \
4*x *(3 + x) *\3*(3 + 2*x)  + 2*x*(3 + x)/
$$4 x^{2} \left(x + 3\right)^{2} \cdot \left(2 x \left(x + 3\right) + 3 \left(2 x + 3\right)^{2}\right)$$
Simplify
The third derivative [src] 
                       /         2              \
24*x*(3 + x)*(3 + 2*x)*\(3 + 2*x)  + 3*x*(3 + x)/
$$24 x \left(x + 3\right) \left(2 x + 3\right) \left(3 x \left(x + 3\right) + \left(2 x + 3\right)^{2}\right)$$
Simplify
The graph
Derivative of y=(x²+3x)⁴
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