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(2*sin(x)+1,5*cos(x))
The derivative of the function/ (2*sin(x)+1,5*cos(x))

Derivative of (2*sin(x)+1,5*cos(x))

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

You have entered [src] 
           3*cos(x)
2*sin(x) + --------
              2
2sin⁡(x)+3cos⁡(x)22 \sin{\left(x \right)} + \frac{3 \cos{\left(x \right)}}{2} 
d /           3*cos(x)\
--|2*sin(x) + --------|
dx\              2    /
ddx(2sin⁡(x)+3cos⁡(x)2)\frac{d}{d x} \left(2 \sin{\left(x \right)} + \frac{3 \cos{\left(x \right)}}{2}\right)
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Detail solution

  1. Differentiate 2sin⁡(x)+3cos⁡(x)22 \sin{\left(x \right)} + \frac{3 \cos{\left(x \right)}}{2} 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: 2cos⁡(x)2 \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)2- \frac{3 \sin{\left(x \right)}}{2}

    The result is: −3sin⁡(x)2+2cos⁡(x)- \frac{3 \sin{\left(x \right)}}{2} + 2 \cos{\left(x \right)}

The answer is:

−3sin⁡(x)2+2cos⁡(x)- \frac{3 \sin{\left(x \right)}}{2} + 2 \cos{\left(x \right)}

The graph
02468-8-6-4-2-10105-5
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
           3*sin(x)
2*cos(x) - --------
              2
−3sin⁡(x)2+2cos⁡(x)- \frac{3 \sin{\left(x \right)}}{2} + 2 \cos{\left(x \right)}
Simplify
The second derivative [src] 
 /           3*cos(x)\
-|2*sin(x) + --------|
 \              2    /
−(2sin⁡(x)+3cos⁡(x)2)- (2 \sin{\left(x \right)} + \frac{3 \cos{\left(x \right)}}{2})
Simplify
The third derivative [src] 
            3*sin(x)
-2*cos(x) + --------
               2
3sin⁡(x)2−2cos⁡(x)\frac{3 \sin{\left(x \right)}}{2} - 2 \cos{\left(x \right)}
Simplify
The graph
Derivative of (2*sin(x)+1,5*cos(x))
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