Mister Exam

Other calculators

y=6x^2-10x-5x^-2
The derivative of the function/ y=6x^2-10x-5x^-2

Derivative of y=6x^2-10x-5x^-2

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   2          5 
6*x  - 10*x - --
               2
              x
$$6 x^{2} - 10 x - \frac{5}{x^{2}}$$ 
d /   2          5 \
--|6*x  - 10*x - --|
dx|               2|
  \              x /
$$\frac{d}{d x} \left(6 x^{2} - 10 x - \frac{5}{x^{2}}\right)$$
Transform
Detail solution

  1. Differentiate 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: goes to

      So, the result is:

    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: goes to

        So, the result is:

      So, the result is:

    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: goes to

        So, the result is:

      So, the result is:

    The result is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
      10       
-10 + -- + 12*x
       3       
      x
$$12 x - 10 + \frac{10}{x^{3}}$$
Simplify
The second derivative [src] 
  /    5 \
6*|2 - --|
  |     4|
  \    x /
$$6 \cdot \left(2 - \frac{5}{x^{4}}\right)$$
Simplify
The third derivative [src] 
120
---
  5
 x
$$\frac{120}{x^{5}}$$
Simplify
The graph
Derivative of y=6x^2-10x-5x^-2
    © Mister Exam – Calculator