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Derivative of:
Derivative of e^(sin(1-3*x)^(2))
Derivative of x×ln(x)
Derivative of x^3-48x+17
Derivative of tg(x)^3
Identical expressions
sqrt(x)+ two *cosx
square root of (x) plus 2 multiply by co sinus of e of x
square root of (x) plus two multiply by co sinus of e of x
√(x)+2*cosx
sqrt(x)+2cosx
sqrtx+2cosx
Similar expressions
sqrt(x)-2*cosx

The derivative of the function/ sqrt(x)+2*cosx

Derivative of sqrt(x)+2*cosx

The solution

You have entered [src]

  ___           
\/ x  + 2*cos(x)

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

sqrt(x) + 2*cos(x)

Detail solution

Differentiate $\sqrt{x} + 2 \cos{\left(x \right)}$ term by term:
1. Apply the power rule: $\sqrt{x}$ goes to $\frac{1}{2 \sqrt{x}}$
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: $- 2 \sin{\left(x \right)} + \frac{1}{2 \sqrt{x}}$

The answer is:

$- 2 \sin{\left(x \right)} + \frac{1}{2 \sqrt{x}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   1              
------- - 2*sin(x)
    ___           
2*\/ x

$$- 2 \sin{\left(x \right)} + \frac{1}{2 \sqrt{x}}$$

Simplify

The second derivative [src]

 /             1   \
-|2*cos(x) + ------|
 |              3/2|
 \           4*x   /

$$- (2 \cos{\left(x \right)} + \frac{1}{4 x^{\frac{3}{2}}})$$

Simplify

The third derivative [src]

             3   
2*sin(x) + ------
              5/2
           8*x

$$2 \sin{\left(x \right)} + \frac{3}{8 x^{\frac{5}{2}}}$$

Simplify