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Derivative of:
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Derivative of x^3-3*x^2
Identical expressions
y=log5* three ^x^ one / two
y equally logarithm of 5 multiply by 3 to the power of x to the power of 1 divide by 2
y equally logarithm of 5 multiply by three to the power of x to the power of one divide by two
y=log5*3x1/2
y=log53^x^1/2
y=log53x1/2
y=log5*3^x^1 divide by 2
What you mean?
log(5)^(3^(x^(13/2)))

The derivative of the function/ y=log5*3^x^1/2

You entered:

y=log5*3^x^1/2

What you mean?

log(5)^(3^(x^(13/2)))

Derivative of y=log5*3^x^1/2

The solution

You have entered [src]

          ___
        \/ x 
log(5)*3

$$3^{\sqrt{x}} \log{\left(5 \right)}$$

  /          ___\
d |        \/ x |
--\log(5)*3     /
dx

$$\frac{d}{d x} 3^{\sqrt{x}} \log{\left(5 \right)}$$

Transform

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = \sqrt{x}$ .
2. $\frac{d}{d u} 3^{u} = 3^{u} \log{\left(3 \right)}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \sqrt{x}$ :
  1. Apply the power rule: $\sqrt{x}$ goes to $\frac{1}{2 \sqrt{x}}$
  The result of the chain rule is:
  
  $\frac{3^{\sqrt{x}} \log{\left(3 \right)}}{2 \sqrt{x}}$
So, the result is: $\frac{3^{\sqrt{x}} \log{\left(3 \right)} \log{\left(5 \right)}}{2 \sqrt{x}}$

The answer is:

$\frac{3^{\sqrt{x}} \log{\left(3 \right)} \log{\left(5 \right)}}{2 \sqrt{x}}$

The graph

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The first derivative [src]

   ___              
 \/ x               
3     *log(3)*log(5)
--------------------
          ___       
      2*\/ x

$$\frac{3^{\sqrt{x}} \log{\left(3 \right)} \log{\left(5 \right)}}{2 \sqrt{x}}$$

Simplify

The second derivative [src]

   ___                                
 \/ x  /   1     log(3)\              
3     *|- ---- + ------|*log(3)*log(5)
       |   3/2     x   |              
       \  x            /              
--------------------------------------
                  4

$$\frac{3^{\sqrt{x}} \left(\frac{\log{\left(3 \right)}}{x} - \frac{1}{x^{\frac{3}{2}}}\right) \log{\left(3 \right)} \log{\left(5 \right)}}{4}$$

Simplify

The third derivative [src]

   ___ /          2              \              
 \/ x  | 3     log (3)   3*log(3)|              
3     *|---- + ------- - --------|*log(3)*log(5)
       | 5/2      3/2        2   |              
       \x        x          x    /              
------------------------------------------------
                       8

$$\frac{3^{\sqrt{x}} \left(- \frac{3 \log{\left(3 \right)}}{x^{2}} + \frac{\log{\left(3 \right)}^{2}}{x^{\frac{3}{2}}} + \frac{3}{x^{\frac{5}{2}}}\right) \log{\left(3 \right)} \log{\left(5 \right)}}{8}$$

Simplify

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What you mean?

Derivative of y=log5*3^x^1/2

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