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Derivative of:
Derivative of 1/3*x^3
Derivative of x^2/(x^2+1)
Derivative of x*sqrt(3-x)
Derivative of (x^2+25)/x
Identical expressions
(x^ three - two)(x^ two + one)
(x cubed minus 2)(x squared plus 1)
(x to the power of three minus two)(x to the power of two plus one)
(x3-2)(x2+1)
x3-2x2+1
(x³-2)(x²+1)
(x to the power of 3-2)(x to the power of 2+1)
x^3-2x^2+1
Similar expressions
(x^3+2)(x^2+1)
(x^3-2)(x^2-1)
y=x^4+5*x^3-2*x^2+1

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

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

The solution

You have entered [src]

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

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

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

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

Transform

Detail solution

Apply the product rule:

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

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

  /        3       /     2\\
2*\-2 + 7*x  + 3*x*\1 + x //

$$2 \cdot \left(7 x^{3} + 3 x \left(x^{2} + 1\right) - 2\right)$$

Simplify

The third derivative [src]

  /        2\
6*\1 + 10*x /

$$6 \cdot \left(10 x^{2} + 1\right)$$

Simplify

The graph

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