Mister Exam

Derivative of y=sinx-ln3x

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
sin(x) - log(3*x)
$$- \log{\left(3 x \right)} + \sin{\left(x \right)}$$
sin(x) - log(3*x)
Detail solution
  1. Differentiate term by term:

    1. The derivative of sine is cosine:

    2. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Let .

      2. The derivative of is .

      3. Then, apply the chain rule. Multiply by :

        1. The derivative of a constant times a function is the constant times the derivative of the function.

          1. Apply the power rule: goes to

          So, the result is:

        The result of the chain rule is:

      So, the result is:

    The result is:


The answer is:

The graph
The first derivative [src]
  1         
- - + cos(x)
  x         
$$\cos{\left(x \right)} - \frac{1}{x}$$
The second derivative [src]
1          
-- - sin(x)
 2         
x          
$$- \sin{\left(x \right)} + \frac{1}{x^{2}}$$
3-я производная [src]
 /2          \
-|-- + cos(x)|
 | 3         |
 \x          /
$$- (\cos{\left(x \right)} + \frac{2}{x^{3}})$$
The third derivative [src]
 /2          \
-|-- + cos(x)|
 | 3         |
 \x          /
$$- (\cos{\left(x \right)} + \frac{2}{x^{3}})$$
The graph
Derivative of y=sinx-ln3x