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Derivative of:
Derivative of tanh(x)
Derivative of (x^5+1)
Derivative of tanx
Derivative of tg2x
Canonical form:
3*sin(x)+x^2-1
Identical expressions
three *sin(x)+x^ two - one
3 multiply by sinus of (x) plus x squared minus 1
three multiply by sinus of (x) plus x to the power of two minus one
3*sin(x)+x2-1
3*sinx+x2-1
3*sin(x)+x²-1
3*sin(x)+x to the power of 2-1
3sin(x)+x^2-1
3sin(x)+x2-1
3sinx+x2-1
3sinx+x^2-1
Similar expressions
3*sin(x)+x^2+1
3*sin(x)-x^2-1
3*sinx+x^2-1

The derivative of the function/ 3*sin(x)+x^2-1

Derivative of 3*sin(x)+x^2-1

The solution

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            2    
3*sin(x) + x  - 1

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

3*sin(x) + x^2 - 1

Detail solution

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

2*x + 3*cos(x)

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

Simplify

The second derivative [src]

2 - 3*sin(x)

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

Simplify

The third derivative [src]

-3*cos(x)

$$- 3 \cos{\left(x \right)}$$

Simplify