Derivative of (5x-6)*cosx

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(5*x - 6)*cos(x)

$$\left(5 x - 6\right) \cos{\left(x \right)}$$

(5*x - 6)*cos(x)

Detail solution

Apply the product rule:

$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$

$f{\left(x \right)} = 5 x - 6$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $5 x - 6$ 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: $5$
  2. The derivative of the constant $-6$ is zero.
  The result is: $5$
$g{\left(x \right)} = \cos{\left(x \right)}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. The derivative of cosine is negative sine:
  
  $\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$
The result is: $- \left(5 x - 6\right) \sin{\left(x \right)} + 5 \cos{\left(x \right)}$
Now simplify:

$\left(6 - 5 x\right) \sin{\left(x \right)} + 5 \cos{\left(x \right)}$

The answer is:

$\left(6 - 5 x\right) \sin{\left(x \right)} + 5 \cos{\left(x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

5*cos(x) - (5*x - 6)*sin(x)

$$- \left(5 x - 6\right) \sin{\left(x \right)} + 5 \cos{\left(x \right)}$$

Simplify

The second derivative [src]

-(10*sin(x) + (-6 + 5*x)*cos(x))

$$- (\left(5 x - 6\right) \cos{\left(x \right)} + 10 \sin{\left(x \right)})$$

Simplify

The third derivative [src]

-15*cos(x) + (-6 + 5*x)*sin(x)

$$\left(5 x - 6\right) \sin{\left(x \right)} - 15 \cos{\left(x \right)}$$

Simplify

The graph