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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
v

The graph:

from to

Piecewise:

The solution

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

  1. Differentiate term by term:

    1. The derivative of sine is cosine:

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

      1. Apply the power rule: goes to

      So, the result is:

    The result is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     3            
- ------- + cos(x)
      ___         
  2*\/ x
$$\cos{\left(x \right)} - \frac{3}{2 \sqrt{x}}$$
Simplify
The second derivative [src] 
            3   
-sin(x) + ------
             3/2
          4*x
$$- \sin{\left(x \right)} + \frac{3}{4 x^{\frac{3}{2}}}$$
Simplify
The third derivative [src] 
 /  9            \
-|------ + cos(x)|
 |   5/2         |
 \8*x            /
$$- (\cos{\left(x \right)} + \frac{9}{8 x^{\frac{5}{2}}})$$
Simplify
The graph
Derivative of y=sinx-3sqrtx
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