Mister Exam

Lang:

Other calculators

y=3x^4-2x^2+x-5

How to use it?
Derivative of:
Derivative of 27x
Derivative of y=csc(2x²)
Derivative of y=3x^4-2x^2+x-5
Derivative of y=sin(2x^2-3)
Identical expressions
y=3x^ four - two x^2+x- five
y equally 3x to the power of 4 minus 2x squared plus x minus 5
y equally 3x to the power of four minus two x squared plus x minus five
y=3x4-2x2+x-5
y=3x⁴-2x²+x-5
y=3x to the power of 4-2x to the power of 2+x-5
Similar expressions
y=3x^4+2x^2+x-5
y=3x^4-2x^2+x+5
y=3x^4-2x^2-x-5

The derivative of the function/ y=3x^4-2x^2+x-5

Derivative of y=3x^4-2x^2+x-5

The solution

You have entered [src]

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

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

3*x^4 - 2*x^2 + x - 5

Detail solution

Differentiate $\left(x + \left(3 x^{4} - 2 x^{2}\right)\right) - 5$ term by term:
1. Differentiate $x + \left(3 x^{4} - 2 x^{2}\right)$ term by term:
  1. Differentiate $3 x^{4} - 2 x^{2}$ term by term:
    1. The derivative of a constant times a function is the constant times the derivative of the function.
      1. Apply the power rule: $x^{4}$ goes to $4 x^{3}$
      So, the result is: $12 x^{3}$
    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: $- 4 x$
    The result is: $12 x^{3} - 4 x$
  2. Apply the power rule: $x$ goes to $1$
  The result is: $12 x^{3} - 4 x + 1$
2. The derivative of the constant $-5$ is zero.
The result is: $12 x^{3} - 4 x + 1$

The answer is:

$12 x^{3} - 4 x + 1$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

              3
1 - 4*x + 12*x

$$12 x^{3} - 4 x + 1$$

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

72*x

$$72 x$$

Simplify

The graph

Derivative of y=3x^4-2x^2+x-5