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Derivative of:
Derivative of cos(5-3*x)
Derivative of arctg^2(3x)
Derivative of cos^3(t)
Derivative of asin(y^2)
Identical expressions
- three *(y)- six *log(y)
minus 3 multiply by (y) minus 6 multiply by logarithm of (y)
minus three multiply by (y) minus six multiply by logarithm of (y)
-3(y)-6log(y)
-3y-6logy
Similar expressions
3*(y)-6*log(y)
-3*(y)+6*log(y)

The derivative of the function/ -3*(y)-6*log(y)

Derivative of -3(y)-6log(y)

The solution

You have entered [src]

-3*y - 6*log(y)

$$- 3 y - 6 \log{\left(y \right)}$$

-3*y - 6*log(y)

Detail solution

Differentiate $- 3 y - 6 \log{\left(y \right)}$ 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: $y$ goes to $1$
  So, the result is: $-3$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. The derivative of $\log{\left(y \right)}$ is $\frac{1}{y}$ .
  So, the result is: $- \frac{6}{y}$
The result is: $-3 - \frac{6}{y}$

The answer is:

$-3 - \frac{6}{y}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     6
-3 - -
     y

$$-3 - \frac{6}{y}$$

Simplify

The second derivative [src]

6 
--
 2
y

$$\frac{6}{y^{2}}$$

Simplify

The third derivative [src]

-12 
----
  3 
 y

$$- \frac{12}{y^{3}}$$

Simplify