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The derivative of the function/ 5cosx+3sinx

Derivative of 5cosx+3sinx

The solution

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

$$3 \sin{\left(x \right)} + 5 \cos{\left(x \right)}$$

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

Detail solution

Differentiate $3 \sin{\left(x \right)} + 5 \cos{\left(x \right)}$ 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 cosine is negative sine:
    
    $\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$
  So, the result is: $- 5 \sin{\left(x \right)}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. The derivative of sine is cosine:
    
    $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
  So, the result is: $3 \cos{\left(x \right)}$
The result is: $- 5 \sin{\left(x \right)} + 3 \cos{\left(x \right)}$

The answer is:

$- 5 \sin{\left(x \right)} + 3 \cos{\left(x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-5*sin(x) + 3*cos(x)

$$- 5 \sin{\left(x \right)} + 3 \cos{\left(x \right)}$$

Simplify

The second derivative [src]

-(3*sin(x) + 5*cos(x))

$$- (3 \sin{\left(x \right)} + 5 \cos{\left(x \right)})$$

Simplify

The third derivative [src]

-3*cos(x) + 5*sin(x)

$$5 \sin{\left(x \right)} - 3 \cos{\left(x \right)}$$

Simplify