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Derivative of:
Derivative of e^x^x
Derivative of ln(x+3)^3
Derivative of cos(3*x)^(2)
Derivative of -cos(2*x)
Identical expressions
x(x^ three +4x^ two - one)
x(x cubed plus 4x squared minus 1)
x(x to the power of three plus 4x to the power of two minus one)
x(x3+4x2-1)
xx3+4x2-1
x(x³+4x²-1)
x(x to the power of 3+4x to the power of 2-1)
xx^3+4x^2-1
Similar expressions
x(x^3-4x^2-1)
x(x^3+4x^2+1)

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

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

The solution

You have entered [src]

  / 3      2    \
x*\x  + 4*x  - 1/

$$x \left(x^{3} + 4 x^{2} - 1\right)$$

d /  / 3      2    \\
--\x*\x  + 4*x  - 1//
dx

$$\frac{d}{d x} x \left(x^{3} + 4 x^{2} - 1\right)$$

Transform

Detail solution

Apply the product rule:

$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$

$f{\left(x \right)} = x$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. Apply the power rule: $x$ goes to $1$
$g{\left(x \right)} = x^{3} + 4 x^{2} - 1$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $x^{3} + 4 x^{2} - 1$ 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: $8 x$
  3. The derivative of the constant $\left(-1\right) 1$ is zero.
  The result is: $3 x^{2} + 8 x$
The result is: $x^{3} + 4 x^{2} + x \left(3 x^{2} + 8 x\right) - 1$
Now simplify:

$4 x^{3} + 12 x^{2} - 1$

The answer is:

$4 x^{3} + 12 x^{2} - 1$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

      3      2     /   2      \
-1 + x  + 4*x  + x*\3*x  + 8*x/

$$x^{3} + 4 x^{2} + x \left(3 x^{2} + 8 x\right) - 1$$

Simplify

The second derivative [src]

2*x*(12 + 6*x)

$$2 x \left(6 x + 12\right)$$

Simplify

The third derivative [src]

6*(4 + 4*x)

$$6 \cdot \left(4 x + 4\right)$$

Simplify

The graph

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