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The derivative of the function/ 3cosx-5sinx

Derivative of 3cosx-5sinx

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

You have entered [src] 
3*cos(x) - 5*sin(x)
−5sin⁡(x)+3cos⁡(x)- 5 \sin{\left(x \right)} + 3 \cos{\left(x \right)} 
3*cos(x) - 5*sin(x)
Detail solution

  1. Differentiate −5sin⁡(x)+3cos⁡(x)- 5 \sin{\left(x \right)} + 3 \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:

        ddxcos⁡(x)=−sin⁡(x)\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}

      So, the result is: −3sin⁡(x)- 3 \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:

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

      So, the result is: −5cos⁡(x)- 5 \cos{\left(x \right)}

    The result is: −3sin⁡(x)−5cos⁡(x)- 3 \sin{\left(x \right)} - 5 \cos{\left(x \right)}

The answer is:

−3sin⁡(x)−5cos⁡(x)- 3 \sin{\left(x \right)} - 5 \cos{\left(x \right)}

The graph
02468-8-6-4-2-1010-1010
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
-5*cos(x) - 3*sin(x)
−3sin⁡(x)−5cos⁡(x)- 3 \sin{\left(x \right)} - 5 \cos{\left(x \right)}
Simplify
The second derivative [src] 
-3*cos(x) + 5*sin(x)
5sin⁡(x)−3cos⁡(x)5 \sin{\left(x \right)} - 3 \cos{\left(x \right)}
Simplify
The third derivative [src] 
3*sin(x) + 5*cos(x)
3sin⁡(x)+5cos⁡(x)3 \sin{\left(x \right)} + 5 \cos{\left(x \right)}
Simplify
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