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y=3sinx+cosx
The derivative of the function/ y=3sinx+cosx

Derivative of y=3sinx+cosx

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

The graph:

from to

Piecewise:

The solution

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

  1. Differentiate 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:

      So, the result is:

    2. The derivative of cosine is negative sine:

    The result is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
-sin(x) + 3*cos(x)
$$- \sin{\left(x \right)} + 3 \cos{\left(x \right)}$$
Simplify
The second derivative [src] 
-(3*sin(x) + cos(x))
$$- (3 \sin{\left(x \right)} + \cos{\left(x \right)})$$
Simplify
The third derivative [src] 
-3*cos(x) + sin(x)
$$\sin{\left(x \right)} - 3 \cos{\left(x \right)}$$
Simplify
The graph
Derivative of y=3sinx+cosx
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