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The derivative of the function/ y=sinx-3cosx+1

Derivative of y=sinx-3cosx+1

The solution

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sin(x) - 3*cos(x) + 1

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

sin(x) - 3*cos(x) + 1

Detail solution

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

3*sin(x) + cos(x)

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

Simplify

The second derivative [src]

-sin(x) + 3*cos(x)

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

Simplify

The third derivative [src]

-(3*sin(x) + cos(x))

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

Simplify

The graph

Derivative of y=sinx-3cosx+1