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Derivative of:
Derivative of 1/3*x^3-4*x
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Derivative of sin(3)^(2)*x
Identical expressions
three x^ four +4x^3- nine /2x
3x to the power of 4 plus 4x cubed minus 9 divide by 2x
three x to the power of four plus 4x cubed minus nine divide by 2x
3x4+4x3-9/2x
3x⁴+4x³-9/2x
3x to the power of 4+4x to the power of 3-9/2x
3x^4+4x^3-9 divide by 2x
Similar expressions
3x^4+4x^3+9/2x
3x^4-4x^3-9/2x

The derivative of the function/ 3x^4+4x^3-9/2x

Derivative of 3x^4+4x^3-9/2x

The solution

You have entered [src]

   4      3   9*x
3*x  + 4*x  - ---
               2

$$3 x^{4} + 4 x^{3} - \frac{9 x}{2}$$

d /   4      3   9*x\
--|3*x  + 4*x  - ---|
dx\               2 /

$$\frac{d}{d x} \left(3 x^{4} + 4 x^{3} - \frac{9 x}{2}\right)$$

Transform

Detail solution

Differentiate $3 x^{4} + 4 x^{3} - \frac{9 x}{2}$ 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: $x^{4}$ goes to $4 x^{3}$
  So, the result is: $12 x^{3}$
2. 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: $12 x^{2}$
3. The derivative of a constant times a function is the constant times the derivative of the function.
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x$ goes to $1$
    So, the result is: $\frac{9}{2}$
  So, the result is: $- \frac{9}{2}$
The result is: $12 x^{3} + 12 x^{2} - \frac{9}{2}$

The answer is:

$12 x^{3} + 12 x^{2} - \frac{9}{2}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  9       2       3
- - + 12*x  + 12*x 
  2

$$12 x^{3} + 12 x^{2} - \frac{9}{2}$$

Simplify

The second derivative [src]

12*x*(2 + 3*x)

$$12 x \left(3 x + 2\right)$$

Simplify

The third derivative [src]

24*(1 + 3*x)

$$24 \cdot \left(3 x + 1\right)$$

Simplify

The graph

Derivative of 3x^4+4x^3-9/2x