Mister Exam

Derivative of 103sinx-105x+65

Function f() - derivative -N order at the point
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The graph:

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Piecewise:

The solution

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103*sin(x) - 105*x + 65
(105x+103sin(x))+65\left(- 105 x + 103 \sin{\left(x \right)}\right) + 65
103*sin(x) - 105*x + 65
Detail solution
  1. Differentiate (105x+103sin(x))+65\left(- 105 x + 103 \sin{\left(x \right)}\right) + 65 term by term:

    1. Differentiate 105x+103sin(x)- 105 x + 103 \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:

          ddxsin(x)=cos(x)\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}

        So, the result is: 103cos(x)103 \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: xx goes to 11

        So, the result is: 105-105

      The result is: 103cos(x)105103 \cos{\left(x \right)} - 105

    2. The derivative of the constant 6565 is zero.

    The result is: 103cos(x)105103 \cos{\left(x \right)} - 105


The answer is:

103cos(x)105103 \cos{\left(x \right)} - 105

The graph
02468-8-6-4-2-1010-25002500
The first derivative [src]
-105 + 103*cos(x)
103cos(x)105103 \cos{\left(x \right)} - 105
The second derivative [src]
-103*sin(x)
103sin(x)- 103 \sin{\left(x \right)}
The third derivative [src]
-103*cos(x)
103cos(x)- 103 \cos{\left(x \right)}