Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of ln5
Derivative of xe^(3x)
Derivative of secx^3
Derivative of 2x^3-sin(3*x)
Identical expressions
2x^ three -sin(three *x)
2x cubed minus sinus of (3 multiply by x)
2x to the power of three minus sinus of (three multiply by x)
2x3-sin(3*x)
2x3-sin3*x
2x³-sin(3*x)
2x to the power of 3-sin(3*x)
2x^3-sin(3x)
2x3-sin(3x)
2x3-sin3x
2x^3-sin3x
Similar expressions
2x^3+sin(3*x)

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

Derivative of 2x^3-sin(3*x)

The solution

You have entered [src]

   3           
2*x  - sin(3*x)

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

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

Detail solution

Differentiate $2 x^{3} - \sin{\left(3 x \right)}$ 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: $x^{3}$ goes to $3 x^{2}$
  So, the result is: $6 x^{2}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = 3 x$ .
  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 $\frac{d}{d x} 3 x$ :
    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: $3$
    The result of the chain rule is:
    
    $3 \cos{\left(3 x \right)}$
  So, the result is: $- 3 \cos{\left(3 x \right)}$
The result is: $6 x^{2} - 3 \cos{\left(3 x \right)}$

The answer is:

$6 x^{2} - 3 \cos{\left(3 x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

                 2
-3*cos(3*x) + 6*x

$$6 x^{2} - 3 \cos{\left(3 x \right)}$$

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

3*(4 + 9*cos(3*x))

$$3 \left(9 \cos{\left(3 x \right)} + 4\right)$$

Simplify