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-7*x^5-8*x^4-2*sin(x)
The derivative of the function/ -7*x^5-8*x^4-2*sin(x)

Derivative of -7*x^5-8*x^4-2*sin(x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
     5      4           
- 7*x  - 8*x  - 2*sin(x)
$$- 7 x^{5} - 8 x^{4} - 2 \sin{\left(x \right)}$$ 
d /     5      4           \
--\- 7*x  - 8*x  - 2*sin(x)/
dx
$$\frac{d}{d x} \left(- 7 x^{5} - 8 x^{4} - 2 \sin{\left(x \right)}\right)$$
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. The derivative of sine is cosine:

        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] 
      4       3           
- 35*x  - 32*x  - 2*cos(x)
$$- 35 x^{4} - 32 x^{3} - 2 \cos{\left(x \right)}$$
Simplify
The second derivative [src] 
  /      3       2         \
2*\- 70*x  - 48*x  + sin(x)/
$$2 \left(- 70 x^{3} - 48 x^{2} + \sin{\left(x \right)}\right)$$
Simplify
The third derivative [src] 
  /       2                \
2*\- 210*x  - 96*x + cos(x)/
$$2 \left(- 210 x^{2} - 96 x + \cos{\left(x \right)}\right)$$
Simplify
The graph
Derivative of -7*x^5-8*x^4-2*sin(x)
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