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Derivative of:
Derivative of e^(2-x)
Derivative of (3-2*x)*cos(x)+2*sin(x)+4
Derivative of e^sin(x)^(2)
Derivative of (cos(x))^sin(x)
Graphing y =:
3x^4-4x^3
Identical expressions
three x^ four -4x^3
3x to the power of 4 minus 4x cubed
three x to the power of four minus 4x cubed
3x4-4x3
3x⁴-4x³
3x to the power of 4-4x to the power of 3
Similar expressions
3x^4+4x^3

The derivative of the function/ 3x^4-4x^3

Derivative of 3x^4-4x^3

The solution

You have entered [src]

   4      3
3*x  - 4*x

$$3 x^{4} - 4 x^{3}$$

d /   4      3\
--\3*x  - 4*x /
dx

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

Transform

Detail solution

Differentiate $3 x^{4} - 4 x^{3}$ 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: $x^{4}$ 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. 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: $12 x^{2}$
  So, the result is: $- 12 x^{2}$
The result is: $12 x^{3} - 12 x^{2}$
Now simplify:

$12 x^{2} \left(x - 1\right)$

The answer is:

$12 x^{2} \left(x - 1\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

      2       3
- 12*x  + 12*x

$$12 x^{3} - 12 x^{2}$$

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