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Identical expressions
y=-x^ three +4x+ five
y equally minus x cubed plus 4x plus 5
y equally minus x to the power of three plus 4x plus five
y=-x3+4x+5
y=-x³+4x+5
y=-x to the power of 3+4x+5
Similar expressions
y=-x^3-4x+5
y=+x^3+4x+5
y=-x^3+4x-5

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

Derivative of y=-x^3+4x+5

The solution

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   3          
- x  + 4*x + 5

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

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

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

Transform

Detail solution

Differentiate $- x^{3} + 4 x + 5$ 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: $- 3 x^{2}$
2. 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: $4$
3. The derivative of the constant $5$ is zero.
The result is: $4 - 3 x^{2}$

The answer is:

$4 - 3 x^{2}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

       2
4 - 3*x

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

Simplify

The second derivative [src]

-6*x

$$- 6 x$$

Simplify

The third derivative [src]

-6

$$-6$$

Simplify

The graph

Derivative of y=-x^3+4x+5