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Identical expressions
two x^ three -5x^2+ four
2x cubed minus 5x squared plus 4
two x to the power of three minus 5x squared plus four
2x3-5x2+4
2x³-5x²+4
2x to the power of 3-5x to the power of 2+4
Similar expressions
2x^3+5x^2+4
2x^3-5x^2-4

The derivative of the function/ 2x^3-5x^2+4

Derivative of 2x^3-5x^2+4

The solution

You have entered [src]

   3      2    
2*x  - 5*x  + 4

$$2 x^{3} - 5 x^{2} + 4$$

d /   3      2    \
--\2*x  - 5*x  + 4/
dx

$$\frac{d}{d x} \left(2 x^{3} - 5 x^{2} + 4\right)$$

Transform

Detail solution

Differentiate $2 x^{3} - 5 x^{2} + 4$ 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: $6 x^{2}$
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: $x^{2}$ goes to $2 x$
    So, the result is: $10 x$
  So, the result is: $- 10 x$
3. The derivative of the constant $4$ is zero.
The result is: $6 x^{2} - 10 x$
Now simplify:

$2 x \left(3 x - 5\right)$

The answer is:

$2 x \left(3 x - 5\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

           2
-10*x + 6*x

$$6 x^{2} - 10 x$$

Simplify

The second derivative [src]

2*(-5 + 6*x)

$$2 \cdot \left(6 x - 5\right)$$

Simplify

The third derivative [src]

$$12$$

Simplify

The graph

Derivative of 2x^3-5x^2+4