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10/x^(2/3)+15*x
The derivative of the function/ 10/x^(2/3)+15*x

Derivative of 10/x^(2/3)+15*x

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

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The solution

You have entered [src] 
 10        
---- + 15*x
 2/3       
x
15x+10x2315 x + \frac{10}{x^{\frac{2}{3}}} 
d / 10        \
--|---- + 15*x|
dx| 2/3       |
  \x          /
ddx(15x+10x23)\frac{d}{d x} \left(15 x + \frac{10}{x^{\frac{2}{3}}}\right)
Transform
Detail solution

  1. Differentiate 15x+10x2315 x + \frac{10}{x^{\frac{2}{3}}} term by term:

    1. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Let u=x23u = x^{\frac{2}{3}}.

      2. Apply the power rule: 1u\frac{1}{u} goes to −1u2- \frac{1}{u^{2}}

      3. Then, apply the chain rule. Multiply by ddxx23\frac{d}{d x} x^{\frac{2}{3}}:

        1. Apply the power rule: x23x^{\frac{2}{3}} goes to 23x3\frac{2}{3 \sqrt[3]{x}}

        The result of the chain rule is:

        −23x53- \frac{2}{3 x^{\frac{5}{3}}}

      So, the result is: −203x53- \frac{20}{3 x^{\frac{5}{3}}}

    2. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the power rule: xx goes to 11

      So, the result is: 1515

    The result is: 15−203x5315 - \frac{20}{3 x^{\frac{5}{3}}}

The answer is:

15−203x5315 - \frac{20}{3 x^{\frac{5}{3}}}

The graph
02468-8-6-4-2-1010-500500
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
       20  
15 - ------
        5/3
     3*x
15−203x5315 - \frac{20}{3 x^{\frac{5}{3}}}
Simplify
The second derivative [src] 
 100  
------
   8/3
9*x
1009x83\frac{100}{9 x^{\frac{8}{3}}}
Simplify
The third derivative [src] 
 -800   
--------
    11/3
27*x
−80027x113- \frac{800}{27 x^{\frac{11}{3}}}
Simplify
The graph
Derivative of 10/x^(2/3)+15*x
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