Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of sqrt(x-1)/(sqrt(x^2-x)-1)
Derivative of cot(x)/x
Derivative of cos(x)/e^x
Derivative of asin(x/2)
Identical expressions
y=x^ four -x^ two +2x+ three
y equally x to the power of 4 minus x squared plus 2x plus 3
y equally x to the power of four minus x to the power of two plus 2x plus three
y=x4-x2+2x+3
y=x⁴-x²+2x+3
y=x to the power of 4-x to the power of 2+2x+3
Similar expressions
y=x^4+x^2+2x+3
y=x^4-x^2-2x+3
y=x^4-x^2+2x-3

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

Derivative of y=x^4-x^2+2x+3

The solution

You have entered [src]

 4    2          
x  - x  + 2*x + 3

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

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

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

Transform

Detail solution

Differentiate $x^{4} - x^{2} + 2 x + 3$ 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: $- 2 x$
3. 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: $2$
4. The derivative of the constant $3$ is zero.
The result is: $4 x^{3} - 2 x + 2$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

             3
2 - 2*x + 4*x

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

Simplify

The second derivative [src]

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

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

Simplify

3-th derivative [src]

24*x

$$24 x$$

Simplify

The third derivative [src]

24*x

$$24 x$$

Simplify

The graph

Derivative of y=x^4-x^2+2x+3