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5sinx-cosx
The derivative of the function/ 5sinx-cosx

Derivative of 5sinx-cosx

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

The graph:

from to

Piecewise:

The solution

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

      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 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] 
5*cos(x) + sin(x)
$$\sin{\left(x \right)} + 5 \cos{\left(x \right)}$$
Simplify
The second derivative [src] 
-5*sin(x) + cos(x)
$$- 5 \sin{\left(x \right)} + \cos{\left(x \right)}$$
Simplify
The third derivative [src] 
-(5*cos(x) + sin(x))
$$- (\sin{\left(x \right)} + 5 \cos{\left(x \right)})$$
Simplify
The graph
Derivative of 5sinx-cosx
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