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The derivative of the function/ f(x)=4x²-5x³+9x

Derivative of f(x)=4x²-5x³+9x

The solution

You have entered [src]

   2      3      
4*x  - 5*x  + 9*x

$$- 5 x^{3} + 4 x^{2} + 9 x$$

d /   2      3      \
--\4*x  - 5*x  + 9*x/
dx

$$\frac{d}{d x} \left(- 5 x^{3} + 4 x^{2} + 9 x\right)$$

Transform

Detail solution

Differentiate $- 5 x^{3} + 4 x^{2} + 9 x$ 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: $x^{2}$ goes to $2 x$
  So, the result is: $8 x$
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: $15 x^{2}$
  So, the result is: $- 15 x^{2}$
3. 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: $9$
The result is: $- 15 x^{2} + 8 x + 9$

The answer is:

$- 15 x^{2} + 8 x + 9$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

        2      
9 - 15*x  + 8*x

$$- 15 x^{2} + 8 x + 9$$

Simplify

The second derivative [src]

2*(4 - 15*x)

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

Simplify

3-th derivative [src]

-30

$$-30$$

Simplify

The third derivative [src]

-30

$$-30$$

Simplify

The graph

Derivative of f(x)=4x²-5x³+9x