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Derivative of:
Derivative of 5-7x
Derivative of 2*sqrt(x^3)
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Identical expressions
three *cbrt(x)-(one /x)+ one
3 multiply by cubic root of (x) minus (1 divide by x) plus 1
three multiply by cubic root of (x) minus (one divide by x) plus one
3cbrt(x)-(1/x)+1
3cbrtx-1/x+1
3*cbrt(x)-(1 divide by x)+1
Similar expressions
(3*cbrtx)-(1/x)+1
3*cbrt(x)-(1/x)-1
3*cbrt(x)+(1/x)+1

The derivative of the function/ 3*cbrt(x)-(1/x)+1

Derivative of 3*cbrt(x)-(1/x)+1

The solution

You have entered [src]

  3 ___   1    
3*\/ x  - - + 1
          x

$$\left(3 \sqrt[3]{x} - \frac{1}{x}\right) + 1$$

3*x^(1/3) - 1/x + 1

Detail solution

Differentiate $\left(3 \sqrt[3]{x} - \frac{1}{x}\right) + 1$ term by term:
1. Differentiate $3 \sqrt[3]{x} - \frac{1}{x}$ term by term:
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $\sqrt[3]{x}$ goes to $\frac{1}{3 x^{\frac{2}{3}}}$
    So, the result is: $\frac{1}{x^{\frac{2}{3}}}$
  2. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $\frac{1}{x}$ goes to $- \frac{1}{x^{2}}$
    So, the result is: $\frac{1}{x^{2}}$
  The result is: $\frac{1}{x^{2}} + \frac{1}{x^{\frac{2}{3}}}$
2. The derivative of the constant $1$ is zero.
The result is: $\frac{1}{x^{2}} + \frac{1}{x^{\frac{2}{3}}}$

The answer is:

$\frac{1}{x^{2}} + \frac{1}{x^{\frac{2}{3}}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

1     1  
-- + ----
 2    2/3
x    x

$$\frac{1}{x^{2}} + \frac{1}{x^{\frac{2}{3}}}$$

Simplify

The second derivative [src]

   /1      1   \
-2*|-- + ------|
   | 3      5/3|
   \x    3*x   /

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

Simplify

The third derivative [src]

  /3      5   \
2*|-- + ------|
  | 4      8/3|
  \x    9*x   /

$$2 \left(\frac{3}{x^{4}} + \frac{5}{9 x^{\frac{8}{3}}}\right)$$

Simplify