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y=lnx/4-3cosx
The derivative of the function/ y=lnx/4-3cosx

Derivative of y=lnx/4-3cosx

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
log(x)           
------ - 3*cos(x)
  4
$$\frac{\log{\left(x \right)}}{4} - 3 \cos{\left(x \right)}$$ 
log(x)/4 - 3*cos(x)
Detail solution

  1. Differentiate term by term:

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

      1. The derivative of is .

      So, the result is:

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

      1. The derivative of cosine is negative sine:

      So, the result is:

    The result is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
            1 
3*sin(x) + ---
           4*x
$$3 \sin{\left(x \right)} + \frac{1}{4 x}$$
Simplify
The second derivative [src] 
            1  
3*cos(x) - ----
              2
           4*x
$$3 \cos{\left(x \right)} - \frac{1}{4 x^{2}}$$
Simplify
The third derivative [src] 
 1             
---- - 3*sin(x)
   3           
2*x
$$- 3 \sin{\left(x \right)} + \frac{1}{2 x^{3}}$$
Simplify
The graph
Derivative of y=lnx/4-3cosx
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