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Graphing y =:
11^(x^2+5x+14)
Identical expressions
eleven ^(x^ two +5x+ fourteen)
11 to the power of (x squared plus 5x plus 14)
eleven to the power of (x to the power of two plus 5x plus fourteen)
11(x2+5x+14)
11x2+5x+14
11^(x²+5x+14)
11 to the power of (x to the power of 2+5x+14)
11^x^2+5x+14
Similar expressions
11^(x^2+5x-14)
11^(x^2-5x+14)

The derivative of the function/ 11^(x^2+5x+14)

Derivative of 11^(x^2+5x+14)

The solution

You have entered [src]

   2           
  x  + 5*x + 14
11

$$11^{\left(x^{2} + 5 x\right) + 14}$$

11^(x^2 + 5*x + 14)

Detail solution

Let $u = \left(x^{2} + 5 x\right) + 14$ .
$\frac{d}{d u} 11^{u} = 11^{u} \log{\left(11 \right)}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(\left(x^{2} + 5 x\right) + 14\right)$ :
1. Differentiate $\left(x^{2} + 5 x\right) + 14$ term by term:
  1. Differentiate $x^{2} + 5 x$ 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: $5$
    The result is: $2 x + 5$
  2. The derivative of the constant $14$ is zero.
  The result is: $2 x + 5$
The result of the chain rule is:

$11^{\left(x^{2} + 5 x\right) + 14} \left(2 x + 5\right) \log{\left(11 \right)}$
Now simplify:

$11^{x \left(x + 5\right) + 14} \left(2 x + 5\right) \log{\left(11 \right)}$

The answer is:

$11^{x \left(x + 5\right) + 14} \left(2 x + 5\right) \log{\left(11 \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   2                             
  x  + 5*x + 14                  
11             *(5 + 2*x)*log(11)

$$11^{\left(x^{2} + 5 x\right) + 14} \left(2 x + 5\right) \log{\left(11 \right)}$$

Simplify

The second derivative [src]

                  x*(5 + x) /             2        \        
379749833583241*11         *\2 + (5 + 2*x) *log(11)/*log(11)

$$379749833583241 \cdot 11^{x \left(x + 5\right)} \left(\left(2 x + 5\right)^{2} \log{\left(11 \right)} + 2\right) \log{\left(11 \right)}$$

Simplify

The third derivative [src]

                  x*(5 + x)    2               /             2        \
379749833583241*11         *log (11)*(5 + 2*x)*\6 + (5 + 2*x) *log(11)/

$$379749833583241 \cdot 11^{x \left(x + 5\right)} \left(2 x + 5\right) \left(\left(2 x + 5\right)^{2} \log{\left(11 \right)} + 6\right) \log{\left(11 \right)}^{2}$$

Simplify

The graph

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Derivative of 11^(x^2+5x+14)

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The solution