Mister Exam

# Derivative of f(x)=(6x²+7x)⁴

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

from to

### The solution

You have entered [src]
            4
/   2      \
\6*x  + 7*x/ 
$$\left(6 x^{2} + 7 x\right)^{4}$$
  /            4\
d |/   2      \ |
--\\6*x  + 7*x/ /
dx               
$$\frac{d}{d x} \left(6 x^{2} + 7 x\right)^{4}$$
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)/
$$12 x^{2} \left(6 x + 7\right)^{2} \cdot \left(4 x \left(6 x + 7\right) + \left(12 x + 7\right)^{2}\right)$$
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