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Derivative of:
Derivative of x^2*e^x
Derivative of x^2*cos(x)
Derivative of e^(5*x)
Derivative of x/(x^2+1)
Identical expressions
three *sin(three *x- one)
3 multiply by sinus of (3 multiply by x minus 1)
three multiply by sinus of (three multiply by x minus one)
3sin(3x-1)
3sin3x-1
Similar expressions
3*sin(3*x+1)

The derivative of the function/ 3*sin(3*x-1)

Derivative of 3sin(3x-1)

The solution

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3*sin(3*x - 1)

$$3 \sin{\left(3 x - 1 \right)}$$

3*sin(3*x - 1)

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = 3 x - 1$ .
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 $\frac{d}{d x} \left(3 x - 1\right)$ :
  1. Differentiate $3 x - 1$ 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: $3$
    2. The derivative of the constant $-1$ is zero.
    The result is: $3$
  The result of the chain rule is:
  
  $3 \cos{\left(3 x - 1 \right)}$
So, the result is: $9 \cos{\left(3 x - 1 \right)}$
Now simplify:

$9 \cos{\left(3 x - 1 \right)}$

The answer is:

$9 \cos{\left(3 x - 1 \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

9*cos(3*x - 1)

$$9 \cos{\left(3 x - 1 \right)}$$

Simplify

The second derivative [src]

-27*sin(-1 + 3*x)

$$- 27 \sin{\left(3 x - 1 \right)}$$

Simplify

The third derivative [src]

-81*cos(-1 + 3*x)

$$- 81 \cos{\left(3 x - 1 \right)}$$

Simplify