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Derivative of:
Derivative of x^3*cot(x)
Derivative of e^sin(x)*cos(x)
Derivative of e^(sin(x)-2*x^3)
Derivative of e^cot(x)
Identical expressions
two *x+ one / three *x+ one
2 multiply by x plus 1 divide by 3 multiply by x plus 1
two multiply by x plus one divide by three multiply by x plus one
2x+1/3x+1
2*x+1 divide by 3*x+1
Similar expressions
2*x+1/3*x-1
2*x-1/3*x+1

The derivative of the function/ 2*x+1/3*x+1

Derivative of 2x+1/3x+1

The solution

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      x    
2*x + - + 1
      3

\left(\frac{x}{3} + 2 x\right) + 1

2*x + x/3 + 1

Detail solution

Differentiate $\left(\frac{x}{3} + 2 x\right) + 1$ term by term:
1. Differentiate $\frac{x}{3} + 2 x$ 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: $x$ goes to $1$
    So, the result is: $2$
  2. 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: $\frac{1}{3}$
  The result is: $\frac{7}{3}$
2. The derivative of the constant $1$ is zero.
The result is: $\frac{7}{3}$

The answer is:

\frac{7}{3}

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

7/3

\frac{7}{3}

Simplify

The second derivative [src]

0

Simplify

The third derivative [src]

0

Simplify