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Derivative of:
Derivative of -e^x
Derivative of 1/2*sqrt(x)
Derivative of x-7
Derivative of x^5-5*x^3-20*x
Identical expressions
(one / four)*sin(two *x+ three)
(1 divide by 4) multiply by sinus of (2 multiply by x plus 3)
(one divide by four) multiply by sinus of (two multiply by x plus three)
(1/4)sin(2x+3)
1/4sin2x+3
(1 divide by 4)*sin(2*x+3)
Similar expressions
(1/4)*sin(2*x-3)

The derivative of the function/ (1/4)*sin(2*x+3)

Derivative of (1/4)sin(2x+3)

The solution

You have entered [src]

sin(2*x + 3)
------------
     4

$$\frac{\sin{\left(2 x + 3 \right)}}{4}$$

sin(2*x + 3)/4

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = 2 x + 3$ .
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 $\frac{d}{d x} \left(2 x + 3\right)$ :
  1. Differentiate $2 x + 3$ 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 $3$ is zero.
    The result is: $2$
  The result of the chain rule is:
  
  $2 \cos{\left(2 x + 3 \right)}$
So, the result is: $\frac{\cos{\left(2 x + 3 \right)}}{2}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

-sin(3 + 2*x)

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

Simplify

The third derivative [src]

-2*cos(3 + 2*x)

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

Simplify