Mister Exam

Derivative of f(x)=(6x²+7x)⁴

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

The graph:

from to

Enter:

The solution

You have entered [src]
            4
/   2      \ 
\6*x  + 7*x/ 
$$\left(6 x^{2} + 7 x\right)^{4}$$
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 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
The first derivative [src]
            3            
/   2      \             
\6*x  + 7*x/ *(28 + 48*x)
$$\left(48 x + 28\right) \left(6 x^{2} + 7 x\right)^{3}$$
The second derivative [src]
    2          2 /          2                \
12*x *(7 + 6*x) *\(7 + 12*x)  + 4*x*(7 + 6*x)/
$$12 x^{2} \left(6 x + 7\right)^{2} \left(4 x \left(6 x + 7\right) + \left(12 x + 7\right)^{2}\right)$$
The third derivative [src]
                          /          2                 \
24*x*(7 + 6*x)*(7 + 12*x)*\(7 + 12*x)  + 18*x*(7 + 6*x)/
$$24 x \left(6 x + 7\right) \left(12 x + 7\right) \left(18 x \left(6 x + 7\right) + \left(12 x + 7\right)^{2}\right)$$
The graph
Derivative of f(x)=(6x²+7x)⁴
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