Mister Exam

Derivative of 5sinx+3cosx

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
5*sin(x) + 3*cos(x)
$$5 \sin{\left(x \right)} + 3 \cos{\left(x \right)}$$
d                      
--(5*sin(x) + 3*cos(x))
dx                     
$$\frac{d}{d x} \left(5 \sin{\left(x \right)} + 3 \cos{\left(x \right)}\right)$$
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
The first derivative [src]
-3*sin(x) + 5*cos(x)
$$- 3 \sin{\left(x \right)} + 5 \cos{\left(x \right)}$$
The second derivative [src]
-(3*cos(x) + 5*sin(x))
$$- (5 \sin{\left(x \right)} + 3 \cos{\left(x \right)})$$
The third derivative [src]
-5*cos(x) + 3*sin(x)
$$3 \sin{\left(x \right)} - 5 \cos{\left(x \right)}$$
The graph
Derivative of 5sinx+3cosx