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Derivative of (x-2)^3
Derivative of sqrt(x^2-1)
Derivative of ln(x)/x
Graphing y =:
2x^3-3x^2+5
Identical expressions
two x^ three -3x^2+ five
2x cubed minus 3x squared plus 5
two x to the power of three minus 3x squared plus five
2x3-3x2+5
2x³-3x²+5
2x to the power of 3-3x to the power of 2+5
Similar expressions
2x^3+3x^2+5
2x^3-3x^2-5

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

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

The solution

You have entered [src]

   3      2    
2*x  - 3*x  + 5

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

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

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

Transform

Detail solution

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

$6 x \left(x - 1\right)$

The answer is:

$6 x \left(x - 1\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

          2
-6*x + 6*x

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

Simplify

The second derivative [src]

6*(-1 + 2*x)

$$6 \cdot \left(2 x - 1\right)$$

Simplify

The third derivative [src]

$$12$$

Simplify

The graph

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