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

Derivative of x^3/2x+4

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

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The solution

You have entered [src] 
 3      
x       
--*x + 4
2
xx32+4x \frac{x^{3}}{2} + 4 
(x^3/2)*x + 4
Detail solution

  1. Differentiate xx32+4x \frac{x^{3}}{2} + 4 term by term:

    1. Apply the quotient rule, which is:

      ddxf(x)g(x)=−f(x)ddxg(x)+g(x)ddxf(x)g2(x)\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}

      f(x)=x4f{\left(x \right)} = x^{4} and g(x)=2g{\left(x \right)} = 2.

      To find ddxf(x)\frac{d}{d x} f{\left(x \right)}:

      1. Apply the power rule: x4x^{4} goes to 4x34 x^{3}

      To find ddxg(x)\frac{d}{d x} g{\left(x \right)}:

      1. The derivative of the constant 22 is zero.

      Now plug in to the quotient rule:

      2x32 x^{3}

    2. The derivative of the constant 44 is zero.

    The result is: 2x32 x^{3}

The answer is:

2x32 x^{3}

The graph
02468-8-6-4-2-1010-1000010000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
   3    3
3*x    x 
---- + --
 2     2
x32+3x32\frac{x^{3}}{2} + \frac{3 x^{3}}{2}
Simplify
The second derivative [src] 
   2
6*x
6x26 x^{2}
Simplify
The third derivative [src] 
12*x
12x12 x
Simplify
The graph
Derivative of x^3/2x+4
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