Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

     d
  ((——•4)•((2x2+5)3))•4x
    dx

Step  2  :

             d
 Simplify   ——
            dx

Canceling Out :

 2.1    Canceling out d as it appears on both sides of the fraction line

Equation at the end of step  2  :

    1
  ((— • 4) • (2x2 + 5)3) • 4x
    x

Step  3  :

Polynomial Roots Calculator :

 3.1    Find roots (zeroes) of :       F(x) = (2x²+5)³
Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  2  and the Trailing Constant is  5.

 The factor(s) are:

of the Leading Coefficient :  1,2
 of the Trailing Constant :  1 ,5

 Let us test ....

Polynomial Roots Calculator found no rational roots

Equation at the end of step  3  :

  4 • (2x2 + 5)3
  —————————————— • 4x
        x       

Step  4  :

Canceling Out :

 4.1    Canceling out x as it appears on both sides of the fraction line

Final result :

  16 • (2x2 + 5)3