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Derivative of:
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Identical expressions
three *x^ two +sin(x)
3 multiply by x squared plus sinus of (x)
three multiply by x to the power of two plus sinus of (x)
3*x2+sin(x)
3*x2+sinx
3*x²+sin(x)
3*x to the power of 2+sin(x)
3x^2+sin(x)
3x2+sin(x)
3x2+sinx
3x^2+sinx
Similar expressions
3*x^2-sin(x)
3*x^2+sinx

The derivative of the function/ 3*x^2+sin(x)

Derivative of 3*x^2+sin(x)

The solution

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   2         
3*x  + sin(x)

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

d /   2         \
--\3*x  + sin(x)/
dx

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

Transform

Detail solution

Differentiate $3 x^{2} + \sin{\left(x \right)}$ 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: $6 x$
2. The derivative of sine is cosine:
  
  $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
The result is: $6 x + \cos{\left(x \right)}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

6*x + cos(x)

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

Simplify

The second derivative [src]

6 - sin(x)

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

Simplify

The third derivative [src]

-cos(x)

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

Simplify

The graph

Derivative of 3*x^2+sin(x)