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Derivative of:
Derivative of x^-3
Derivative of x^2*sqrt(x)
Derivative of x^2*e^x
Derivative of 1/2*x^2
Identical expressions
x^ four +3x^ two -2x+ one
x to the power of 4 plus 3x squared minus 2x plus 1
x to the power of four plus 3x to the power of two minus 2x plus one
x4+3x2-2x+1
x⁴+3x²-2x+1
x to the power of 4+3x to the power of 2-2x+1
Similar expressions
x^4+3*x^2-2*x+1
x^4-3x^2-2x+1
x^4+3x^2+2x+1
x^4+3x^2-2x-1

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

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

The solution

You have entered [src]

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

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

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

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

Transform

Detail solution

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

The answer is:

$4 x^{3} + 6 x - 2$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

        3      
-2 + 4*x  + 6*x

$$4 x^{3} + 6 x - 2$$

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

24*x

$$24 x$$

Simplify

The graph

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