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The derivative of the function/ 8sqrtx+7sin(x)

Derivative of 8sqrtx+7sin(x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
    ___           
8*\/ x  + 7*sin(x)
$$8 \sqrt{x} + 7 \sin{\left(x \right)}$$ 
8*sqrt(x) + 7*sin(x)
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. Apply the power rule: goes to

      So, the result is:

    2. 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:

    The result is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  4             
----- + 7*cos(x)
  ___           
\/ x
$$7 \cos{\left(x \right)} + \frac{4}{\sqrt{x}}$$
Simplify
The second derivative [src] 
 / 2             \
-|---- + 7*sin(x)|
 | 3/2           |
 \x              /
$$- (7 \sin{\left(x \right)} + \frac{2}{x^{\frac{3}{2}}})$$
Simplify
The third derivative [src] 
             3  
-7*cos(x) + ----
             5/2
            x
$$- 7 \cos{\left(x \right)} + \frac{3}{x^{\frac{5}{2}}}$$
Simplify
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