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The derivative of the function/ f(x)=4sinx+5cosx

Derivative of f(x)=4sinx+5cosx

The solution

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

$$4 \sin{\left(x \right)} + 5 \cos{\left(x \right)}$$

d                      
--(4*sin(x) + 5*cos(x))
dx

$$\frac{d}{d x} \left(4 \sin{\left(x \right)} + 5 \cos{\left(x \right)}\right)$$

Transform

Detail solution

Differentiate $4 \sin{\left(x \right)} + 5 \cos{\left(x \right)}$ 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 sine is cosine:
    
    $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
  So, the result is: $4 \cos{\left(x \right)}$
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: $- 5 \sin{\left(x \right)}$
The result is: $- 5 \sin{\left(x \right)} + 4 \cos{\left(x \right)}$

The answer is:

$- 5 \sin{\left(x \right)} + 4 \cos{\left(x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-5*sin(x) + 4*cos(x)

$$- 5 \sin{\left(x \right)} + 4 \cos{\left(x \right)}$$

Simplify

The second derivative [src]

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

$$- (4 \sin{\left(x \right)} + 5 \cos{\left(x \right)})$$

Simplify

The third derivative [src]

-4*cos(x) + 5*sin(x)

$$5 \sin{\left(x \right)} - 4 \cos{\left(x \right)}$$

Simplify

The graph

Derivative of f(x)=4sinx+5cosx