Mister Exam

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The derivative of the function/ sinx+3cosx

Derivative of sinx+3cosx

The solution

You have entered [src]

sin(x) + 3*cos(x)

$$\sin{\left(x \right)} + 3 \cos{\left(x \right)}$$

sin(x) + 3*cos(x)

Detail solution

Differentiate $\sin{\left(x \right)} + 3 \cos{\left(x \right)}$ term by term:
1. The derivative of sine is cosine:
  
  $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
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:
    
    $\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$
  So, the result is: $- 3 \sin{\left(x \right)}$
The result is: $- 3 \sin{\left(x \right)} + \cos{\left(x \right)}$

The answer is:

$- 3 \sin{\left(x \right)} + \cos{\left(x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-3*sin(x) + cos(x)

$$- 3 \sin{\left(x \right)} + \cos{\left(x \right)}$$

Simplify

The second derivative [src]

-(3*cos(x) + sin(x))

$$- (\sin{\left(x \right)} + 3 \cos{\left(x \right)})$$

Simplify

The third derivative [src]

-cos(x) + 3*sin(x)

$$3 \sin{\left(x \right)} - \cos{\left(x \right)}$$

Simplify