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13*x-10*sin(x)+1

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Identical expressions
thirteen *x- ten *sin(x)+ one
13 multiply by x minus 10 multiply by sinus of (x) plus 1
thirteen multiply by x minus ten multiply by sinus of (x) plus one
13x-10sin(x)+1
13x-10sinx+1
Similar expressions
13*x-10*sin(x)-1
13*x+10*sin(x)+1
13*x-10*sinx+1

The derivative of the function/ 13*x-10*sin(x)+1

Derivative of 13x-10sin(x)+1

The solution

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13*x - 10*sin(x) + 1

$$\left(13 x - 10 \sin{\left(x \right)}\right) + 1$$

13*x - 10*sin(x) + 1

Detail solution

Differentiate $\left(13 x - 10 \sin{\left(x \right)}\right) + 1$ term by term:
1. Differentiate $13 x - 10 \sin{\left(x \right)}$ 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: $x$ goes to $1$
    So, the result is: $13$
  2. 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: $- 10 \cos{\left(x \right)}$
  The result is: $13 - 10 \cos{\left(x \right)}$
2. The derivative of the constant $1$ is zero.
The result is: $13 - 10 \cos{\left(x \right)}$

The answer is:

$13 - 10 \cos{\left(x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

13 - 10*cos(x)

$$13 - 10 \cos{\left(x \right)}$$

Simplify

The second derivative [src]

10*sin(x)

$$10 \sin{\left(x \right)}$$

Simplify

The third derivative [src]

10*cos(x)

$$10 \cos{\left(x \right)}$$

Simplify

The graph

Derivative of 13*x-10*sin(x)+1