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(2*sin(x)+1,5*cos(x))

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Derivative of:
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Derivative of e^(2-x)
Derivative of x^2-4*x
Identical expressions
(two *sin(x)+ one , five *cos(x))
(2 multiply by sinus of (x) plus 1,5 multiply by co sinus of e of (x))
(two multiply by sinus of (x) plus one , five multiply by co sinus of e of (x))
(2sin(x)+1,5cos(x))
2sinx+1,5cosx
Similar expressions
2*sinx+1,5*cosx
(2*sin(x)-1,5*cos(x))
(2*sinx+1,5*cosx)

The derivative of the function/ (2*sin(x)+1,5*cos(x))

Derivative of (2sin(x)+1,5cos(x))

The solution

You have entered [src]

           3*cos(x)
2*sin(x) + --------
              2

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

d /           3*cos(x)\
--|2*sin(x) + --------|
dx\              2    /

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

Transform

Detail solution

Differentiate $2 \sin{\left(x \right)} + \frac{3 \cos{\left(x \right)}}{2}$ 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: $2 \cos{\left(x \right)}$
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: $- \frac{3 \sin{\left(x \right)}}{2}$
The result is: $- \frac{3 \sin{\left(x \right)}}{2} + 2 \cos{\left(x \right)}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

           3*sin(x)
2*cos(x) - --------
              2

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

            3*sin(x)
-2*cos(x) + --------
               2

$$\frac{3 \sin{\left(x \right)}}{2} - 2 \cos{\left(x \right)}$$

Simplify

The graph

Derivative of (2*sin(x)+1,5*cos(x))