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Derivative of:
Derivative of (1+sqrt(x))/(1-sqrt(x))
Derivative of 12x-ln(12x)+4
Derivative of y=5-4x+7x³-x^5
Derivative of x/(x^2+4)
Identical expressions
sin(x)+sqrt(three)*cos(x)
sinus of (x) plus square root of (3) multiply by co sinus of e of (x)
sinus of (x) plus square root of (three) multiply by co sinus of e of (x)
sin(x)+√(3)*cos(x)
sin(x)+sqrt(3)cos(x)
sinx+sqrt3cosx
Similar expressions
sin(x)-sqrt(3)*cos(x)
sinx+sqrt(3)*cosx

The derivative of the function/ sin(x)+sqrt(3)*cos(x)

Derivative of sin(x)+sqrt(3)*cos(x)

The solution

You have entered [src]

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sin(x) + \/ 3 *cos(x)

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

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

Detail solution

Differentiate $\sin{\left(x \right)} + \sqrt{3} \cos{\left(x \right)}$ 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: $- \sqrt{3} \sin{\left(x \right)}$
The result is: $- \sqrt{3} \sin{\left(x \right)} + \cos{\left(x \right)}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify