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y=sinx-3sqrtx
The derivative of the function/ y=sinx-3sqrtx

Derivative of y=sinx-3sqrtx

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

You have entered [src] 
             ___
sin(x) - 3*\/ x
−3x+sin⁡(x)- 3 \sqrt{x} + \sin{\left(x \right)} 
sin(x) - 3*sqrt(x)
Detail solution

  1. Differentiate −3x+sin⁡(x)- 3 \sqrt{x} + \sin{\left(x \right)} term by term:

    1. The derivative of sine is cosine:

      ddxsin⁡(x)=cos⁡(x)\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}

    2. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the power rule: x\sqrt{x} goes to 12x\frac{1}{2 \sqrt{x}}

      So, the result is: −32x- \frac{3}{2 \sqrt{x}}

    The result is: cos⁡(x)−32x\cos{\left(x \right)} - \frac{3}{2 \sqrt{x}}

The answer is:

cos⁡(x)−32x\cos{\left(x \right)} - \frac{3}{2 \sqrt{x}}

The graph
02468-8-6-4-2-1010-2010
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     3            
- ------- + cos(x)
      ___         
  2*\/ x
cos⁡(x)−32x\cos{\left(x \right)} - \frac{3}{2 \sqrt{x}}
Simplify
The second derivative [src] 
            3   
-sin(x) + ------
             3/2
          4*x
−sin⁡(x)+34x32- \sin{\left(x \right)} + \frac{3}{4 x^{\frac{3}{2}}}
Simplify
The third derivative [src] 
 /  9            \
-|------ + cos(x)|
 |   5/2         |
 \8*x            /
−(cos⁡(x)+98x52)- (\cos{\left(x \right)} + \frac{9}{8 x^{\frac{5}{2}}})
Simplify
The graph
Derivative of y=sinx-3sqrtx
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