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Derivative of:
Derivative of 11*x-log(x+4)^11-3
Derivative of y=x^3-8x^2+10x-4
Derivative of y=12x+√x
Derivative of x+ln(x^2-4)
Identical expressions
five *sin(x)- three *cos(x)
5 multiply by sinus of (x) minus 3 multiply by co sinus of e of (x)
five multiply by sinus of (x) minus three multiply by co sinus of e of (x)
5sin(x)-3cos(x)
5sinx-3cosx
Similar expressions
5*sin(x)+3*cos(x)
5*sinx-3*cosx

The derivative of the function/ 5*sin(x)-3*cos(x)

Derivative of 5sin(x)-3cos(x)

The solution

You have entered [src]

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

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

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

Detail solution

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify