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Derivative of:
Derivative of atan(sqrt(x))
Derivative of 3*x^5
Derivative of 3*x^2*e^x
Derivative of 3*cos(3*x)
Identical expressions
y= four *log2(x)+ eight *x
y equally 4 multiply by logarithm of 2(x) plus 8 multiply by x
y equally four multiply by logarithm of 2(x) plus eight multiply by x
y=4log2(x)+8x
y=4log2x+8x
Similar expressions
y=4*log2(x)-8*x

The derivative of the function/ y=4*log2(x)+8*x

Derivative of y=4log2(x)+8x

The solution

You have entered [src]

  log(x)      
4*------ + 8*x
  log(2)

$$8 x + 4 \frac{\log{\left(x \right)}}{\log{\left(2 \right)}}$$

4*(log(x)/log(2)) + 8*x

Detail solution

Differentiate $8 x + 4 \frac{\log{\left(x \right)}}{\log{\left(2 \right)}}$ 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 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: $\frac{1}{x \log{\left(2 \right)}}$
  So, the result is: $\frac{4}{x \log{\left(2 \right)}}$
2. 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: $8$
The result is: $8 + \frac{4}{x \log{\left(2 \right)}}$

The answer is:

$8 + \frac{4}{x \log{\left(2 \right)}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

       4    
8 + --------
    x*log(2)

$$8 + \frac{4}{x \log{\left(2 \right)}}$$

Simplify

The second derivative [src]

   -4    
---------
 2       
x *log(2)

$$- \frac{4}{x^{2} \log{\left(2 \right)}}$$

Simplify

The third derivative [src]

    8    
---------
 3       
x *log(2)

$$\frac{8}{x^{3} \log{\left(2 \right)}}$$

Simplify