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5sinx+3cosx
The derivative of the function/ 5sinx+3cosx

Derivative of 5sinx+3cosx

Function f() - derivative -N order at the point
v

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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)
Transform
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
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
-3*sin(x) + 5*cos(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] 
-5*cos(x) + 3*sin(x)
3sin⁡(x)−5cos⁡(x)3 \sin{\left(x \right)} - 5 \cos{\left(x \right)}
Simplify
The graph
Derivative of 5sinx+3cosx
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