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3sinx-4cosx
The derivative of the function/ 3sinx-4cosx

Derivative of 3sinx-4cosx

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

You have entered [src] 
3*sin(x) - 4*cos(x)
3sin⁡(x)−4cos⁡(x)3 \sin{\left(x \right)} - 4 \cos{\left(x \right)} 
d                      
--(3*sin(x) - 4*cos(x))
dx
ddx(3sin⁡(x)−4cos⁡(x))\frac{d}{d x} \left(3 \sin{\left(x \right)} - 4 \cos{\left(x \right)}\right)
Transform
Detail solution

  1. Differentiate 3sin⁡(x)−4cos⁡(x)3 \sin{\left(x \right)} - 4 \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: 3cos⁡(x)3 \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 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: −4sin⁡(x)- 4 \sin{\left(x \right)}

      So, the result is: 4sin⁡(x)4 \sin{\left(x \right)}

    The result is: 4sin⁡(x)+3cos⁡(x)4 \sin{\left(x \right)} + 3 \cos{\left(x \right)}

The answer is:

4sin⁡(x)+3cos⁡(x)4 \sin{\left(x \right)} + 3 \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*cos(x) + 4*sin(x)
4sin⁡(x)+3cos⁡(x)4 \sin{\left(x \right)} + 3 \cos{\left(x \right)}
Simplify
The second derivative [src] 
-3*sin(x) + 4*cos(x)
−3sin⁡(x)+4cos⁡(x)- 3 \sin{\left(x \right)} + 4 \cos{\left(x \right)}
Simplify
The third derivative [src] 
-(3*cos(x) + 4*sin(x))
−(4sin⁡(x)+3cos⁡(x))- (4 \sin{\left(x \right)} + 3 \cos{\left(x \right)})
Simplify
The graph
Derivative of 3sinx-4cosx
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