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f(x)=1/3x^3+2x^2-4

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Derivative of:
Derivative of x^(1/3)/(3*x+2)
Derivative of exp(x)*x
Derivative of 1/(x+1)^2
Derivative of x*ln(x)
Sum of series:
f(x)
Integral of d{x}:
f(x)
f(x)
Identical expressions
f(x)= one / three x^3+ two x^2- four
f(x) equally 1 divide by 3x cubed plus 2x squared minus 4
f(x) equally one divide by three x cubed plus two x squared minus four
f(x)=1/3x3+2x2-4
fx=1/3x3+2x2-4
f(x)=1/3x³+2x²-4
f(x)=1/3x to the power of 3+2x to the power of 2-4
fx=1/3x^3+2x^2-4
f(x)=1 divide by 3x^3+2x^2-4
Similar expressions
f(x)=1/3x^3-2x^2-4
f(x)=1/3x^3+2x^2+4

The derivative of the function/ f(x)=1/3x^3+2x^2-4

Derivative of f(x)=1/3x^3+2x^2-4

The solution

You have entered [src]

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

$$\frac{x^{3}}{3} + 2 x^{2} - 4$$

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

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

Transform

Detail solution

Differentiate $\frac{x^{3}}{3} + 2 x^{2} - 4$ 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: $x^{2}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  So, the result is: $4 x$
3. The derivative of the constant $\left(-1\right) 4$ is zero.
The result is: $x^{2} + 4 x$
Now simplify:

$x \left(x + 4\right)$

The answer is:

$x \left(x + 4\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 2      
x  + 4*x

$$x^{2} + 4 x$$

Simplify

The second derivative [src]

2*(2 + x)

$$2 \left(x + 2\right)$$

Simplify

The third derivative [src]

$$2$$

Simplify

The graph

Derivative of f(x)=1/3x^3+2x^2-4