Mister Exam

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Derivative of:
Derivative of x^-2
Derivative of (-1)/x^2
Derivative of e^x^3
Derivative of (x+1)
Graphing y =:
x^3+sinx
Identical expressions
x^ three +sinx
x cubed plus sinus of x
x to the power of three plus sinus of x
x3+sinx
x³+sinx
x to the power of 3+sinx
Similar expressions
x^3-sinx

The derivative of the function/ x^3+sinx

Derivative of x^3+sinx

The solution

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 3         
x  + sin(x)

$$x^{3} + \sin{\left(x \right)}$$

x^3 + sin(x)

Detail solution

Differentiate $x^{3} + \sin{\left(x \right)}$ term by term:
1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
2. The derivative of sine is cosine:
  
  $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
The result is: $3 x^{2} + \cos{\left(x \right)}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   2         
3*x  + cos(x)

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

Simplify

The second derivative [src]

-sin(x) + 6*x

$$6 x - \sin{\left(x \right)}$$

Simplify

The third derivative [src]

6 - cos(x)

$$6 - \cos{\left(x \right)}$$

Simplify