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12*sin(x)-17*x+8

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Derivative of:
Derivative of x^2-7*x
Derivative of (sin(x))^2+(cos(x))^2
Derivative of sqrt(y)
Derivative of sin(2*t)
Graphing y =:
12*sin(x)-17*x+8
Identical expressions
twelve *sin(x)- seventeen *x+ eight
12 multiply by sinus of (x) minus 17 multiply by x plus 8
twelve multiply by sinus of (x) minus seventeen multiply by x plus eight
12sin(x)-17x+8
12sinx-17x+8
Similar expressions
12sinx-17x+8
12*sin(x)+17*x+8
12*sin(x)-17*x-8
12*sinx-17*x+8

The derivative of the function/ 12*sin(x)-17*x+8

Derivative of 12sin(x)-17x+8

The solution

You have entered [src]

12*sin(x) - 17*x + 8

$$\left(- 17 x + 12 \sin{\left(x \right)}\right) + 8$$

12*sin(x) - 17*x + 8

Detail solution

Differentiate $\left(- 17 x + 12 \sin{\left(x \right)}\right) + 8$ term by term:
1. Differentiate $- 17 x + 12 \sin{\left(x \right)}$ term by term:
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. The derivative of sine is cosine:
      
      $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
    So, the result is: $12 \cos{\left(x \right)}$
  2. 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: $-17$
  The result is: $12 \cos{\left(x \right)} - 17$
2. The derivative of the constant $8$ is zero.
The result is: $12 \cos{\left(x \right)} - 17$

The answer is:

$12 \cos{\left(x \right)} - 17$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-17 + 12*cos(x)

$$12 \cos{\left(x \right)} - 17$$

Simplify

The second derivative [src]

-12*sin(x)

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

Simplify

The third derivative [src]

-12*cos(x)

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

Simplify

The graph

Derivative of 12*sin(x)-17*x+8