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Derivative of:
Derivative of 3^-x
Derivative of 1-cost
Derivative of (x+2)*(x^2-4*x+5)
Derivative of (x^2+8)/(x-1)
Identical expressions
- zero . five *sin(2x+ five)
minus 0.5 multiply by sinus of (2x plus 5)
minus zero . five multiply by sinus of (2x plus five)
-0.5sin(2x+5)
-0.5sin2x+5
Similar expressions
-0.5*sin(2x-5)
0.5*sin(2x+5)

The derivative of the function/ -0.5*sin(2x+5)

Derivative of -0.5*sin(2x+5)

The solution

You have entered [src]

-sin(2*x + 5) 
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      2

$$- \frac{\sin{\left(2 x + 5 \right)}}{2}$$

-sin(2*x + 5)/2

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = 2 x + 5$ .
2. The derivative of sine is cosine:
  
  $\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(2 x + 5\right)$ :
  1. Differentiate $2 x + 5$ term by term:
    1. The derivative of a constant times a function is the constant times the derivative of the function.
      1. Apply the power rule: $x$ goes to $1$
      So, the result is: $2$
    2. The derivative of the constant $5$ is zero.
    The result is: $2$
  The result of the chain rule is:
  
  $2 \cos{\left(2 x + 5 \right)}$
So, the result is: $- \cos{\left(2 x + 5 \right)}$
Now simplify:

$- \cos{\left(2 x + 5 \right)}$

The answer is:

$- \cos{\left(2 x + 5 \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-cos(2*x + 5)

$$- \cos{\left(2 x + 5 \right)}$$

Simplify

The second derivative [src]

2*sin(5 + 2*x)

$$2 \sin{\left(2 x + 5 \right)}$$

Simplify

The third derivative [src]

4*cos(5 + 2*x)

$$4 \cos{\left(2 x + 5 \right)}$$

Simplify