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The derivative of the function/ 7cosx-5sinx-9

Derivative of 7cosx-5sinx-9

The solution

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7*cos(x) - 5*sin(x) - 9

$$\left(- 5 \sin{\left(x \right)} + 7 \cos{\left(x \right)}\right) - 9$$

7*cos(x) - 5*sin(x) - 9

Detail solution

Differentiate $\left(- 5 \sin{\left(x \right)} + 7 \cos{\left(x \right)}\right) - 9$ term by term:
1. Differentiate $- 5 \sin{\left(x \right)} + 7 \cos{\left(x \right)}$ 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 cosine is negative sine:
      
      $\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$
    So, the result is: $- 7 \sin{\left(x \right)}$
  2. The derivative of a constant times a function is the constant times the derivative of the function.
    1. The derivative of sine is cosine:
      
      $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
    So, the result is: $- 5 \cos{\left(x \right)}$
  The result is: $- 7 \sin{\left(x \right)} - 5 \cos{\left(x \right)}$
2. The derivative of the constant $-9$ is zero.
The result is: $- 7 \sin{\left(x \right)} - 5 \cos{\left(x \right)}$

The answer is:

$- 7 \sin{\left(x \right)} - 5 \cos{\left(x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-7*sin(x) - 5*cos(x)

$$- 7 \sin{\left(x \right)} - 5 \cos{\left(x \right)}$$

Simplify

The second derivative [src]

-7*cos(x) + 5*sin(x)

$$5 \sin{\left(x \right)} - 7 \cos{\left(x \right)}$$

Simplify

The third derivative [src]

5*cos(x) + 7*sin(x)

$$7 \sin{\left(x \right)} + 5 \cos{\left(x \right)}$$

Simplify

The graph

Derivative of 7cosx-5sinx-9