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Derivative of:
Derivative of sin(4x)
Derivative of x^e
Derivative of (x^3-1)(x^2+x+1)
Derivative of ln1
Identical expressions
y=4sin(x)+(log(x)/log(six))
y equally 4 sinus of (x) plus ( logarithm of (x) divide by logarithm of (6))
y equally 4 sinus of (x) plus ( logarithm of (x) divide by logarithm of (six))
y=4sinx+logx/log6
y=4sin(x)+(log(x) divide by log(6))
Similar expressions
y=4sin(x)-(log(x)/log(6))
y=4sinx+(log(x)/log(6))

The derivative of the function/ y=4sin(x)+(log(x)/log(6))

Derivative of y=4sin(x)+(log(x)/log(6))

The solution

You have entered [src]

           log(x)
4*sin(x) + ------
           log(6)

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

4*sin(x) + log(x)/log(6)

Detail solution

Differentiate $\frac{\log{\left(x \right)}}{\log{\left(6 \right)}} + 4 \sin{\left(x \right)}$ 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 sine is cosine:
    
    $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
  So, the result is: $4 \cos{\left(x \right)}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
  So, the result is: $\frac{1}{x \log{\left(6 \right)}}$
The result is: $4 \cos{\left(x \right)} + \frac{1}{x \log{\left(6 \right)}}$

The answer is:

$4 \cos{\left(x \right)} + \frac{1}{x \log{\left(6 \right)}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

              1    
4*cos(x) + --------
           x*log(6)

$$4 \cos{\left(x \right)} + \frac{1}{x \log{\left(6 \right)}}$$

Simplify

The second derivative [src]

 /               1    \
-|4*sin(x) + ---------|
 |            2       |
 \           x *log(6)/

$$- (4 \sin{\left(x \right)} + \frac{1}{x^{2} \log{\left(6 \right)}})$$

Simplify

The third derivative [src]

  /                1    \
2*|-2*cos(x) + ---------|
  |             3       |
  \            x *log(6)/

$$2 \left(- 2 \cos{\left(x \right)} + \frac{1}{x^{3} \log{\left(6 \right)}}\right)$$

Simplify