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Derivative of:
Derivative of x^5-6*x
Derivative of t-sint
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Derivative of 3x-ln(x+3)^3
Identical expressions
(√x^ four -3x^ two +5x)
(√x to the power of 4 minus 3x squared plus 5x)
(√x to the power of four minus 3x to the power of two plus 5x)
(√x4-3x2+5x)
√x4-3x2+5x
(√x⁴-3x²+5x)
(√x to the power of 4-3x to the power of 2+5x)
√x^4-3x^2+5x
Similar expressions
(√x^4-3x^2-5x)
(√x^4+3x^2+5x)

The derivative of the function/ (√x^4-3x^2+5x)

Derivative of (√x^4-3x^2+5x)

The solution

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

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

  /     4             \
d |  ___       2      |
--\\/ x   - 3*x  + 5*x/
dx

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

Transform

Detail solution

Differentiate $\left(\sqrt{x}\right)^{4} - 3 x^{2} + 5 x$ term by term:
1. Let $u = \sqrt{x}$ .
2. Apply the power rule: $u^{4}$ goes to $4 u^{3}$
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:
  
  $2 x$
4. The derivative of a constant times a function is the constant times the derivative of the function.
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x^{2}$ goes to $2 x$
    So, the result is: $6 x$
  So, the result is: $- 6 x$
5. 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: $5 - 4 x$

The answer is:

$5 - 4 x$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

             2
          2*x 
5 - 6*x + ----
           x

$$\frac{2 x^{2}}{x} - 6 x + 5$$

Simplify

The second derivative [src]

-4

$$-4$$

Simplify

The third derivative [src]

$$0$$

Simplify

The graph

Derivative of (√x^4-3x^2+5x)