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Derivative of:
Derivative of (x+5)/(x+1)
Derivative of x*2^x
Derivative of e^sin(x)*cos(x)
Derivative of atan(3*x)
Identical expressions
sin^ two (2x+ three)
sinus of squared (2x plus 3)
sinus of to the power of two (2x plus three)
sin2(2x+3)
sin22x+3
sin²(2x+3)
sin to the power of 2(2x+3)
sin^22x+3
Similar expressions
sin^2(2x-3)

The derivative of the function/ sin^2(2x+3)

Derivative of sin^2(2x+3)

The solution

You have entered [src]

   2         
sin (2*x + 3)

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

sin(2*x + 3)^2

Detail solution

Let $u = \sin{\left(2 x + 3 \right)}$ .
Apply the power rule: $u^{2}$ goes to $2 u$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \sin{\left(2 x + 3 \right)}$ :
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:
  
  $2 \cos{\left(2 x + 3 \right)}$
The result of the chain rule is:

$4 \sin{\left(2 x + 3 \right)} \cos{\left(2 x + 3 \right)}$
Now simplify:

$2 \sin{\left(4 x + 6 \right)}$

The answer is:

$2 \sin{\left(4 x + 6 \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

$$8 \left(- \sin^{2}{\left(2 x + 3 \right)} + \cos^{2}{\left(2 x + 3 \right)}\right)$$

Simplify

The third derivative [src]

-64*cos(3 + 2*x)*sin(3 + 2*x)

$$- 64 \sin{\left(2 x + 3 \right)} \cos{\left(2 x + 3 \right)}$$

Simplify

The graph

Derivative of sin^2(2x+3)