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Derivative of:
Derivative of asin(t)
Derivative of 7/x^4
Derivative of -(x^2+25)/x
Derivative of (x^2+1)^4
Integral of d{x}:
x^4(x-1)
Identical expressions
x^ four (x- one)
x to the power of 4(x minus 1)
x to the power of four (x minus one)
x4(x-1)
x4x-1
x⁴(x-1)
x^4x-1
Similar expressions
x^4(x+1)

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

Derivative of x^4(x-1)

The solution

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 4        
x *(x - 1)

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

d / 4        \
--\x *(x - 1)/
dx

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

Transform

Detail solution

Apply the product rule:

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

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 4      3        
x  + 4*x *(x - 1)

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

Simplify

The second derivative [src]

   2           
4*x *(-3 + 5*x)

$$4 x^{2} \cdot \left(5 x - 3\right)$$

Simplify

The third derivative [src]

12*x*(-2 + 5*x)

$$12 x \left(5 x - 2\right)$$

Simplify

The graph

Derivative of x^4(x-1)