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Derivative of:
Derivative of x^-3
Derivative of x^2*sqrt(x)
Derivative of 1/2*x^2
Derivative of e^(5*x)
Graphing y =:
x^3+3x^2-4
Identical expressions
x^ three +3x^ two - four
x cubed plus 3x squared minus 4
x to the power of three plus 3x to the power of two minus four
x3+3x2-4
x³+3x²-4
x to the power of 3+3x to the power of 2-4
Similar expressions
x^3+3x^2+4
x^3-3x^2-4

The derivative of the function/ x^3+3x^2-4

Derivative of x^3+3x^2-4

The solution

You have entered [src]

 3      2    
x  + 3*x  - 4

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

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

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

Transform

Detail solution

Differentiate $x^{3} + 3 x^{2} - 4$ term by term:
1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  So, the result is: $6 x$
3. The derivative of the constant $\left(-1\right) 4$ is zero.
The result is: $3 x^{2} + 6 x$
Now simplify:

$3 x \left(x + 2\right)$

The answer is:

$3 x \left(x + 2\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   2      
3*x  + 6*x

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

Simplify

The second derivative [src]

6*(1 + x)

$$6 \left(x + 1\right)$$

Simplify

The third derivative [src]

$$6$$

Simplify

The graph

Derivative of x^3+3x^2-4