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log(5)(x^2-6x+12)

How to use it?
Derivative of:
Derivative of y=5
Derivative of x^6-6x^10+12x
Derivative of log(1+e^x)
Derivative of e^((x^2)-x)
Identical expressions
log(five)(x^ two -6x+ twelve)
logarithm of (5)(x squared minus 6x plus 12)
logarithm of (five)(x to the power of two minus 6x plus twelve)
log(5)(x2-6x+12)
log5x2-6x+12
log(5)(x²-6x+12)
log(5)(x to the power of 2-6x+12)
log5x^2-6x+12
Similar expressions
log(5)(x^2-6x-12)
log(5)(x^2+6x+12)

The derivative of the function/ log(5)(x^2-6x+12)

Derivative of log(5)(x^2-6x+12)

The solution

You have entered [src]

       / 2           \
log(5)*\x  - 6*x + 12/

$$\left(x^{2} - 6 x + 12\right) \log{\left(5 \right)}$$

d /       / 2           \\
--\log(5)*\x  - 6*x + 12//
dx

$$\frac{d}{d x} \left(x^{2} - 6 x + 12\right) \log{\left(5 \right)}$$

Transform

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Differentiate $x^{2} - 6 x + 12$ term by term:
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  2. 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. Apply the power rule: $x$ goes to $1$
      So, the result is: $6$
    So, the result is: $-6$
  3. The derivative of the constant $12$ is zero.
  The result is: $2 x - 6$
So, the result is: $\left(2 x - 6\right) \log{\left(5 \right)}$
Now simplify:

$2 \left(x - 3\right) \log{\left(5 \right)}$

The answer is:

$2 \left(x - 3\right) \log{\left(5 \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

(-6 + 2*x)*log(5)

$$\left(2 x - 6\right) \log{\left(5 \right)}$$

Simplify

The second derivative [src]

2*log(5)

$$2 \log{\left(5 \right)}$$

Simplify

The third derivative [src]

$$0$$

Simplify

The graph

Derivative of log(5)(x^2-6x+12)