Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of 3^x
Derivative of arccos(2x)
Derivative of y=sqrt(cos3x)
Derivative of y=e^-cos5x
Identical expressions
five x^ four -3x^ two +5
5x to the power of 4 minus 3x squared plus 5
five x to the power of four minus 3x to the power of two plus 5
5x4-3x2+5
5x⁴-3x²+5
5x to the power of 4-3x to the power of 2+5
Similar expressions
5x^4+3x^2+5
5x^4-3x^2-5

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

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

The solution

You have entered [src]

   4      2    
5*x  - 3*x  + 5

$$5 x^{4} - 3 x^{2} + 5$$

d /   4      2    \
--\5*x  - 3*x  + 5/
dx

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

Transform

Detail solution

Differentiate $5 x^{4} - 3 x^{2} + 5$ 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: $20 x^{3}$
2. 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: $x^{2}$ goes to $2 x$
    So, the result is: $6 x$
  So, the result is: $- 6 x$
3. The derivative of the constant $5$ is zero.
The result is: $20 x^{3} - 6 x$

The answer is:

$20 x^{3} - 6 x$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

           3
-6*x + 20*x

$$20 x^{3} - 6 x$$

Simplify

The second derivative [src]

  /         2\
6*\-1 + 10*x /

$$6 \cdot \left(10 x^{2} - 1\right)$$

Simplify

The third derivative [src]

120*x

$$120 x$$

Simplify

The graph

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