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y=sqrt(x)+4x^3−6

Derivative of y=sqrt(x)+4x^3−6

Function f() - derivative -N order at the point
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The graph:

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The solution

You have entered [src]
  ___      3    
\/ x  + 4*x  - 6
(x+4x3)6\left(\sqrt{x} + 4 x^{3}\right) - 6
sqrt(x) + 4*x^3 - 6
Detail solution
  1. Differentiate (x+4x3)6\left(\sqrt{x} + 4 x^{3}\right) - 6 term by term:

    1. Differentiate x+4x3\sqrt{x} + 4 x^{3} term by term:

      1. Apply the power rule: x\sqrt{x} goes to 12x\frac{1}{2 \sqrt{x}}

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

        1. Apply the power rule: x3x^{3} goes to 3x23 x^{2}

        So, the result is: 12x212 x^{2}

      The result is: 12x2+12x12 x^{2} + \frac{1}{2 \sqrt{x}}

    2. The derivative of the constant 6-6 is zero.

    The result is: 12x2+12x12 x^{2} + \frac{1}{2 \sqrt{x}}


The answer is:

12x2+12x12 x^{2} + \frac{1}{2 \sqrt{x}}

The graph
02468-8-6-4-2-1010-50005000
The first derivative [src]
   1          2
------- + 12*x 
    ___        
2*\/ x         
12x2+12x12 x^{2} + \frac{1}{2 \sqrt{x}}
The second derivative [src]
         1   
24*x - ------
          3/2
       4*x   
24x14x3224 x - \frac{1}{4 x^{\frac{3}{2}}}
The third derivative [src]
  /      1   \
3*|8 + ------|
  |       5/2|
  \    8*x   /
3(8+18x52)3 \left(8 + \frac{1}{8 x^{\frac{5}{2}}}\right)
The graph
Derivative of y=sqrt(x)+4x^3−6