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(x^2-1)*(x^4+2)

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Derivative of:
Derivative of (x^2-1)*(x^4+2)
Derivative of 5*x^2-2/sqrt(x)+sin(pi/4)
Derivative of 4*sqrt(x)
Derivative of (1+x)
Identical expressions
(x^ two - one)*(x^ four + two)
(x squared minus 1) multiply by (x to the power of 4 plus 2)
(x to the power of two minus one) multiply by (x to the power of four plus two)
(x2-1)*(x4+2)
x2-1*x4+2
(x²-1)*(x⁴+2)
(x to the power of 2-1)*(x to the power of 4+2)
(x^2-1)(x^4+2)
(x2-1)(x4+2)
x2-1x4+2
x^2-1x^4+2
Similar expressions
(x^2+1)*(x^4+2)
(x^2-1)*(x^4-2)

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

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

The solution

You have entered [src]

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

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

(x^2 - 1)*(x^4 + 2)

Detail solution

Apply the product rule:

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

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

$6 x^{5} - 4 x^{3} + 4 x$

The answer is:

$6 x^{5} - 4 x^{3} + 4 x$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

  /       4      2 /      2\\
2*\2 + 9*x  + 6*x *\-1 + x //

$$2 \left(9 x^{4} + 6 x^{2} \left(x^{2} - 1\right) + 2\right)$$

Simplify

The third derivative [src]

     /        2\
24*x*\-1 + 5*x /

$$24 x \left(5 x^{2} - 1\right)$$

Simplify

The graph

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