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The derivative of the function/ y=15sinx-12cosx

Derivative of y=15sinx-12cosx

The solution

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15*sin(x) - 12*cos(x)

$$15 \sin{\left(x \right)} - 12 \cos{\left(x \right)}$$

15*sin(x) - 12*cos(x)

Detail solution

Differentiate $15 \sin{\left(x \right)} - 12 \cos{\left(x \right)}$ 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 sine is cosine:
    
    $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
  So, the result is: $15 \cos{\left(x \right)}$
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: $12 \sin{\left(x \right)}$
The result is: $12 \sin{\left(x \right)} + 15 \cos{\left(x \right)}$

The answer is:

$12 \sin{\left(x \right)} + 15 \cos{\left(x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

12*sin(x) + 15*cos(x)

$$12 \sin{\left(x \right)} + 15 \cos{\left(x \right)}$$

Simplify

The second derivative [src]

3*(-5*sin(x) + 4*cos(x))

$$3 \left(- 5 \sin{\left(x \right)} + 4 \cos{\left(x \right)}\right)$$

Simplify

The third derivative [src]

-3*(4*sin(x) + 5*cos(x))

$$- 3 \left(4 \sin{\left(x \right)} + 5 \cos{\left(x \right)}\right)$$

Simplify