Mister Exam

Lang:

The derivative of the function/ y=3sinx+2cosx

Derivative of y=3sinx+2cosx

The solution

You have entered [src]

3*sin(x) + 2*cos(x)

$$3 \sin{\left(x \right)} + 2 \cos{\left(x \right)}$$

3*sin(x) + 2*cos(x)

Detail solution

Differentiate $3 \sin{\left(x \right)} + 2 \cos{\left(x \right)}$ 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:
    
    $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
  So, the result is: $3 \cos{\left(x \right)}$
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: $- 2 \sin{\left(x \right)}$
The result is: $- 2 \sin{\left(x \right)} + 3 \cos{\left(x \right)}$

The answer is:

$- 2 \sin{\left(x \right)} + 3 \cos{\left(x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-2*sin(x) + 3*cos(x)

$$- 2 \sin{\left(x \right)} + 3 \cos{\left(x \right)}$$

Simplify

The second derivative [src]

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

$$- (3 \sin{\left(x \right)} + 2 \cos{\left(x \right)})$$

Simplify

The third derivative [src]

-3*cos(x) + 2*sin(x)

$$2 \sin{\left(x \right)} - 3 \cos{\left(x \right)}$$

Simplify