Mister Exam

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How to use it?
Derivative of:
Derivative of f(x)=x^2
Derivative of 8lnx
Derivative of x×ln(x)
Derivative of x+ln(x^2-4)
Identical expressions
y=x^(- five)·(x2- three)^ one / four
y equally x to the power of ( minus 5)·(x2 minus 3) to the power of 1 divide by 4
y equally x to the power of ( minus five)·(x2 minus three) to the power of one divide by four
y=x(-5)·(x2-3)1/4
y=x-5·x2-31/4
y=x^-5·x2-3^1/4
y=x^(-5)·(x2-3)^1 divide by 4
Similar expressions
y=x^(-5)·(x2+3)^1/4
y=x^(5)·(x2-3)^1/4
What you mean?
(x^2 - 1*3)^(15/2)/x^5

You entered:

y=x^(-5)·(x2-3)^1/4

(x^2 - 1*3)^(15/2)/x^5

Derivative of y=x^(-5)·(x2-3)^1/4

You have entered [src]

4 ________
\/ x2 - 3 
----------
     5    
    x

$$\frac{\sqrt[4]{x_{2} - 3}}{x^{5}}$$

  /4 ________\
d |\/ x2 - 3 |
--|----------|
dx|     5    |
  \    x     /

$$\frac{\partial}{\partial x} \frac{\sqrt[4]{x_{2} - 3}}{x^{5}}$$

Transform

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Apply the power rule: $\frac{1}{x^{5}}$ goes to $- \frac{5}{x^{6}}$
So, the result is: $- \frac{5 \sqrt[4]{x_{2} - 3}}{x^{6}}$
Now simplify:

$- \frac{5 \sqrt[4]{x_{2} - 3}}{x^{6}}$

The answer is:

$- \frac{5 \sqrt[4]{x_{2} - 3}}{x^{6}}$

The first derivative [src]

   4 ________
-5*\/ x2 - 3 
-------------
       6     
      x

$$- \frac{5 \sqrt[4]{x_{2} - 3}}{x^{6}}$$

Simplify

The second derivative [src]

   4 _________
30*\/ -3 + x2 
--------------
       7      
      x

$$\frac{30 \sqrt[4]{x_{2} - 3}}{x^{7}}$$

Simplify

The third derivative [src]

     4 _________
-210*\/ -3 + x2 
----------------
        8       
       x

$$- \frac{210 \sqrt[4]{x_{2} - 3}}{x^{8}}$$

Simplify