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Derivative of:
Derivative of f(x)=x^2
Derivative of y=2x+3
Derivative of x^(5*x)
Derivative of x^3/(x^2-x+1)
Identical expressions
six / five ^6sqrt(x)^ five
6 divide by 5 to the power of 6 square root of (x) to the power of 5
six divide by five to the power of 6 square root of (x) to the power of five
6/5^6√(x)^5
6/56sqrt(x)5
6/56sqrtx5
6/5⁶sqrt(x)⁵
6/5^6sqrtx^5
6 divide by 5^6sqrt(x)^5

The derivative of the function/ 6/5^6sqrt(x)^5

Derivative of 6/5^6sqrt(x)^5

The solution

You have entered [src]

          5
   6   ___ 
6/5 *\/ x

\left(\frac{6}{5}\right)^{6} \left(\sqrt{x}\right)^{5}

  /          5\
d |   6   ___ |
--\6/5 *\/ x  /
dx

\frac{d}{d x} \left(\frac{6}{5}\right)^{6} \left(\sqrt{x}\right)^{5}

Transform

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = \sqrt{x}$ .
2. Apply the power rule: $u^{5}$ goes to $5 u^{4}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \sqrt{x}$ :
  1. Apply the power rule: $\sqrt{x}$ goes to $\frac{1}{2 \sqrt{x}}$
  The result of the chain rule is:
  
  $\frac{5 x^{\frac{3}{2}}}{2}$
So, the result is: $\frac{23328 x^{\frac{3}{2}}}{3125}$

The answer is:

\frac{23328 x^{\frac{3}{2}}}{3125}

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

       3/2
23328*x   
----------
   3125

\frac{23328 x^{\frac{3}{2}}}{3125}

Simplify

The second derivative [src]

        ___
34992*\/ x 
-----------
    3125

\frac{34992 \sqrt{x}}{3125}

Simplify

The third derivative [src]

  17496   
----------
       ___
3125*\/ x

\frac{17496}{3125 \sqrt{x}}

Simplify

The graph

Derivative of 6/5^6sqrt(x)^5