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The derivative of the function/ f(x)=5x³-4x²-3x+2

Derivative of f(x)=5x³-4x²-3x+2

The solution

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   3      2          
5*x  - 4*x  - 3*x + 2

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

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

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

Transform

Detail solution

Differentiate $5 x^{3} - 4 x^{2} - 3 x + 2$ 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: $x^{3}$ goes to $3 x^{2}$
  So, the result is: $15 x^{2}$
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: $8 x$
  So, the result is: $- 8 x$
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: $3$
  So, the result is: $-3$
4. The derivative of the constant $2$ is zero.
The result is: $15 x^{2} - 8 x - 3$

The answer is:

$15 x^{2} - 8 x - 3$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

               2
-3 - 8*x + 15*x

$$15 x^{2} - 8 x - 3$$

Simplify

The second derivative [src]

2*(-4 + 15*x)

$$2 \cdot \left(15 x - 4\right)$$

Simplify

4-th derivative [src]

$$0$$

Simplify

The third derivative [src]

$$30$$

Simplify

The graph

Derivative of f(x)=5x³-4x²-3x+2