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Derivative of:
Derivative of y=3x-2
Derivative of 2/3*x^3
Derivative of 4/(x^2)
Derivative of 3x^-2
Identical expressions
two / three x^3+ one /2x^ four
2 divide by 3x cubed plus 1 divide by 2x to the power of 4
two divide by three x cubed plus one divide by 2x to the power of four
2/3x3+1/2x4
2/3x³+1/2x⁴
2/3x to the power of 3+1/2x to the power of 4
2 divide by 3x^3+1 divide by 2x^4
Similar expressions
2/3x^3-1/2x^4

The derivative of the function/ 2/3x^3+1/2x^4

Derivative of 2/3x^3+1/2x^4

The solution

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   3    4
2*x    x 
---- + --
 3     2

$$\frac{x^{4}}{2} + \frac{2 x^{3}}{3}$$

  /   3    4\
d |2*x    x |
--|---- + --|
dx\ 3     2 /

$$\frac{d}{d x} \left(\frac{x^{4}}{2} + \frac{2 x^{3}}{3}\right)$$

Transform

Detail solution

Differentiate $\frac{x^{4}}{2} + \frac{2 x^{3}}{3}$ term by term:
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
  So, the result is: $2 x^{2}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x^{4}$ goes to $4 x^{3}$
  So, the result is: $2 x^{3}$
The result is: $2 x^{3} + 2 x^{2}$
Now simplify:

$2 x^{2} \left(x + 1\right)$

The answer is:

$2 x^{2} \left(x + 1\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   2      3
2*x  + 2*x

$$2 x^{3} + 2 x^{2}$$

Simplify

The second derivative [src]

2*x*(2 + 3*x)

$$2 x \left(3 x + 2\right)$$

Simplify

The third derivative [src]

4*(1 + 3*x)

$$4 \cdot \left(3 x + 1\right)$$

Simplify

The graph

Derivative of 2/3x^3+1/2x^4