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Derivative of:
Derivative of 2*x/(x^2+4)
Derivative of sqrt(x)-1/(sqrt(x)*2-x-1)
Derivative of ln(x^2-4x)
Derivative of cos(pi/3-4*x)
Identical expressions
(3x^ two + five)^ four
(3x squared plus 5) to the power of 4
(3x to the power of two plus five) to the power of four
(3x2+5)4
3x2+54
(3x²+5)⁴
(3x to the power of 2+5) to the power of 4
3x^2+5^4
Similar expressions
(3x^2-5)^4

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

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

The solution

You have entered [src]

          4
/   2    \ 
\3*x  + 5/

$$\left(3 x^{2} + 5\right)^{4}$$

(3*x^2 + 5)^4

Detail solution

Let $u = 3 x^{2} + 5$ .
Apply the power rule: $u^{4}$ goes to $4 u^{3}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(3 x^{2} + 5\right)$ :
1. Differentiate $3 x^{2} + 5$ 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: $x^{2}$ goes to $2 x$
    So, the result is: $6 x$
  2. The derivative of the constant $5$ is zero.
  The result is: $6 x$
The result of the chain rule is:

$24 x \left(3 x^{2} + 5\right)^{3}$
Now simplify:

$24 x \left(3 x^{2} + 5\right)^{3}$

The answer is:

$24 x \left(3 x^{2} + 5\right)^{3}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

               3
     /   2    \ 
24*x*\3*x  + 5/

$$24 x \left(3 x^{2} + 5\right)^{3}$$

Simplify

The second derivative [src]

             2            
   /       2\  /        2\
24*\5 + 3*x / *\5 + 21*x /

$$24 \left(3 x^{2} + 5\right)^{2} \left(21 x^{2} + 5\right)$$

Simplify

The third derivative [src]

       /       2\ /       2\
1296*x*\5 + 3*x /*\5 + 7*x /

$$1296 x \left(3 x^{2} + 5\right) \left(7 x^{2} + 5\right)$$

Simplify