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f(x)=1/3x²+x²+2x

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Derivative of:
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Derivative of f(x)=1/3x²+x²+2x
Sum of series:
f(x)
Integral of d{x}:
f(x)
f(x)
Identical expressions
f(x)= one /3x²+x²+2x
f(x) equally 1 divide by 3x² plus x² plus 2x
f(x) equally one divide by 3x² plus x² plus 2x
fx=1/3x²+x²+2x
f(x)=1 divide by 3x²+x²+2x
Similar expressions
f(x)=1/3x²-x²+2x
f(x)=1/3x²+x²-2x

The derivative of the function/ f(x)=1/3x²+x²+2x

Derivative of f(x)=1/3x²+x²+2x

The solution

You have entered [src]

 2           
x     2      
-- + x  + 2*x
3

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

  / 2           \
d |x     2      |
--|-- + x  + 2*x|
dx\3            /

$$\frac{d}{d x} \left(\frac{x^{2}}{3} + x^{2} + 2 x\right)$$

Transform

Detail solution

Differentiate $\frac{x^{2}}{3} + x^{2} + 2 x$ 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: $x^{2}$ goes to $2 x$
  So, the result is: $\frac{2 x}{3}$
2. Apply the power rule: $x^{2}$ goes to $2 x$
3. 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: $2$
The result is: $\frac{8 x}{3} + 2$

The answer is:

$\frac{8 x}{3} + 2$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    8*x
2 + ---
     3

$$\frac{8 x}{3} + 2$$

Simplify

The second derivative [src]

8/3

$$\frac{8}{3}$$

Simplify

The third derivative [src]

$$0$$

Simplify

The graph

Derivative of f(x)=1/3x²+x²+2x