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Identical expressions
y= four ^((x^ two)-14x+ fifty)
y equally 4 to the power of ((x squared ) minus 14x plus 50)
y equally four to the power of ((x to the power of two) minus 14x plus fifty)
y=4((x2)-14x+50)
y=4x2-14x+50
y=4^((x²)-14x+50)
y=4 to the power of ((x to the power of 2)-14x+50)
y=4^x^2-14x+50
Similar expressions
y=4^((x^2)-14x-50)
y=4^((x^2)+14x+50)

The derivative of the function/ y=4^((x^2)-14x+50)

Derivative of y=4^((x^2)-14x+50)

The solution

You have entered [src]

  2            
 x  - 14*x + 50
4

$$4^{\left(x^{2} - 14 x\right) + 50}$$

4^(x^2 - 14*x + 50)

Detail solution

Let $u = \left(x^{2} - 14 x\right) + 50$ .
$\frac{d}{d u} 4^{u} = 4^{u} \log{\left(4 \right)}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(\left(x^{2} - 14 x\right) + 50\right)$ :
1. Differentiate $\left(x^{2} - 14 x\right) + 50$ term by term:
  1. Differentiate $x^{2} - 14 x$ 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: $-14$
    The result is: $2 x - 14$
  2. The derivative of the constant $50$ is zero.
  The result is: $2 x - 14$
The result of the chain rule is:

$4^{\left(x^{2} - 14 x\right) + 50} \left(2 x - 14\right) \log{\left(4 \right)}$
Now simplify:

$2^{2 x \left(x - 14\right) + 102} \left(x - 7\right) \log{\left(2 \right)}$

The answer is:

$2^{2 x \left(x - 14\right) + 102} \left(x - 7\right) \log{\left(2 \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  2                               
 x  - 14*x + 50                   
4              *(-14 + 2*x)*log(4)

$$4^{\left(x^{2} - 14 x\right) + 50} \left(2 x - 14\right) \log{\left(4 \right)}$$

Simplify

The second derivative [src]

                                 x*(-14 + x) /              2       \       
2535301200456458802993406410752*4           *\1 + 2*(-7 + x) *log(4)/*log(4)

$$2535301200456458802993406410752 \cdot 4^{x \left(x - 14\right)} \left(2 \left(x - 7\right)^{2} \log{\left(4 \right)} + 1\right) \log{\left(4 \right)}$$

Simplify

The third derivative [src]

                                 x*(-14 + x)    2             /              2       \
5070602400912917605986812821504*4           *log (4)*(-7 + x)*\3 + 2*(-7 + x) *log(4)/

$$5070602400912917605986812821504 \cdot 4^{x \left(x - 14\right)} \left(x - 7\right) \left(2 \left(x - 7\right)^{2} \log{\left(4 \right)} + 3\right) \log{\left(4 \right)}^{2}$$

Simplify

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Derivative of y=4^((x^2)-14x+50)

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The solution