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y=log*8(x^2+3x)

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Identical expressions
y=log* eight (x^ two +3x)
y equally logarithm of multiply by 8(x squared plus 3x)
y equally logarithm of multiply by eight (x to the power of two plus 3x)
y=log*8(x2+3x)
y=log*8x2+3x
y=log*8(x²+3x)
y=log*8(x to the power of 2+3x)
y=log8(x^2+3x)
y=log8(x2+3x)
y=log8x2+3x
y=log8x^2+3x
Similar expressions
y=log*8(x^2-3x)

The derivative of the function/ y=log*8(x^2+3x)

Derivative of y=log*8(x^2+3x)

The solution

You have entered [src]

       / 2      \
log(8)*\x  + 3*x/

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

log(8)*(x^2 + 3*x)

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Differentiate $x^{2} + 3 x$ 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. Apply the power rule: $x$ goes to $1$
    So, the result is: $3$
  The result is: $2 x + 3$
So, the result is: $\left(2 x + 3\right) \log{\left(8 \right)}$
Now simplify:

$\log{\left(2^{6 x + 9} \right)}$

The answer is:

$\log{\left(2^{6 x + 9} \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

2*log(8)

$$2 \log{\left(8 \right)}$$

Simplify

The third derivative [src]

$$0$$

Simplify

The graph

Derivative of y=log*8(x^2+3x)