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y=x^12+8x^3-2x^2-cosx
The derivative of the function/ y=x^12+8x^3-2x^2-cosx

Derivative of y=x^12+8x^3-2x^2-cosx

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 12      3      2         
x   + 8*x  - 2*x  - cos(x)
$$x^{12} + 8 x^{3} - 2 x^{2} - \cos{\left(x \right)}$$ 
d / 12      3      2         \
--\x   + 8*x  - 2*x  - cos(x)/
dx
$$\frac{d}{d x} \left(x^{12} + 8 x^{3} - 2 x^{2} - \cos{\left(x \right)}\right)$$
Transform
Detail solution

  1. Differentiate term by term:

    1. Apply the power rule: goes to

    2. 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:

    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:

    4. The derivative of a constant times a function is the constant times the derivative of the function.

      1. The derivative of cosine is negative sine:

      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] 
           11       2         
-4*x + 12*x   + 24*x  + sin(x)
$$12 x^{11} + 24 x^{2} - 4 x + \sin{\left(x \right)}$$
Simplify
The second derivative [src] 
                 10         
-4 + 48*x + 132*x   + cos(x)
$$132 x^{10} + 48 x + \cos{\left(x \right)} - 4$$
Simplify
The third derivative [src] 
                    9
48 - sin(x) + 1320*x
$$1320 x^{9} - \sin{\left(x \right)} + 48$$
Simplify
The graph
Derivative of y=x^12+8x^3-2x^2-cosx
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