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The derivative of the function/ y(x)=2x³-3x

Derivative of y(x)=2x³-3x

The solution

You have entered [src]

   3      
2*x  - 3*x

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

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

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

Transform

Detail solution

Differentiate $2 x^{3} - 3 x$ 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: $x$ goes to $1$
    So, the result is: $3$
  So, the result is: $-3$
The result is: $6 x^{2} - 3$

The answer is:

$6 x^{2} - 3$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

        2
-3 + 6*x

$$6 x^{2} - 3$$

Simplify

The second derivative [src]

12*x

$$12 x$$

Simplify

The third derivative [src]

$$12$$

Simplify

The graph

Derivative of y(x)=2x³-3x