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Identical expressions
y=x^ five - three √x
y equally x to the power of 5 minus 3√x
y equally x to the power of five minus three √x
y=x5-3√x
y=x⁵-3√x
Similar expressions
y=x^5+3√x

The derivative of the function/ y=x^5-3√x

Derivative of y=x^5-3√x

The solution

You have entered [src]

 5       ___
x  - 3*\/ x

$$- 3 \sqrt{x} + x^{5}$$

x^5 - 3*sqrt(x)

Detail solution

Differentiate $- 3 \sqrt{x} + x^{5}$ term by term:
1. Apply the power rule: $x^{5}$ goes to $5 x^{4}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $\sqrt{x}$ goes to $\frac{1}{2 \sqrt{x}}$
  So, the result is: $- \frac{3}{2 \sqrt{x}}$
The result is: $5 x^{4} - \frac{3}{2 \sqrt{x}}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   4      3   
5*x  - -------
           ___
       2*\/ x

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

Simplify

The second derivative [src]

    3     3   
20*x  + ------
           3/2
        4*x

$$20 x^{3} + \frac{3}{4 x^{\frac{3}{2}}}$$

Simplify

The third derivative [src]

  /    2     3   \
3*|20*x  - ------|
  |           5/2|
  \        8*x   /

$$3 \left(20 x^{2} - \frac{3}{8 x^{\frac{5}{2}}}\right)$$

Simplify

The graph

Derivative of y=x^5-3√x