Mister Exam

Derivative of 5sinx+3cosx

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

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Piecewise:

The solution

You have entered [src]
5*sin(x) + 3*cos(x)
5sin(x)+3cos(x)5 \sin{\left(x \right)} + 3 \cos{\left(x \right)}
d                      
--(5*sin(x) + 3*cos(x))
dx                     
ddx(5sin(x)+3cos(x))\frac{d}{d x} \left(5 \sin{\left(x \right)} + 3 \cos{\left(x \right)}\right)
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 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)}

    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:

        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)}

    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
The first derivative [src]
-3*sin(x) + 5*cos(x)
3sin(x)+5cos(x)- 3 \sin{\left(x \right)} + 5 \cos{\left(x \right)}
The second derivative [src]
-(3*cos(x) + 5*sin(x))
(5sin(x)+3cos(x))- (5 \sin{\left(x \right)} + 3 \cos{\left(x \right)})
The third derivative [src]
-5*cos(x) + 3*sin(x)
3sin(x)5cos(x)3 \sin{\left(x \right)} - 5 \cos{\left(x \right)}
The graph
Derivative of 5sinx+3cosx