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Derivative of:
Derivative of -2/x
Derivative of x*acos(x)
Derivative of (x^2-1)/(x^2+1)
Derivative of x^2-3x
Identical expressions
y=-3x^ two +13sqrt(x)
y equally minus 3x squared plus 13 square root of (x)
y equally minus 3x to the power of two plus 13 square root of (x)
y=-3x^2+13√(x)
y=-3x2+13sqrt(x)
y=-3x2+13sqrtx
y=-3x²+13sqrt(x)
y=-3x to the power of 2+13sqrt(x)
y=-3x^2+13sqrtx
Similar expressions
y=+3x^2+13sqrt(x)
y=-3x^2-13sqrt(x)

The derivative of the function/ y=-3x^2+13sqrt(x)

Derivative of y=-3x^2+13sqrt(x)

The solution

You have entered [src]

     2        ___
- 3*x  + 13*\/ x

$$13 \sqrt{x} - 3 x^{2}$$

-3*x^2 + 13*sqrt(x)

Detail solution

Differentiate $13 \sqrt{x} - 3 x^{2}$ 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: $x^{2}$ goes to $2 x$
  So, the result is: $- 6 x$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $\sqrt{x}$ goes to $\frac{1}{2 \sqrt{x}}$
  So, the result is: $\frac{13}{2 \sqrt{x}}$
The result is: $- 6 x + \frac{13}{2 \sqrt{x}}$

The answer is:

$- 6 x + \frac{13}{2 \sqrt{x}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

          13  
-6*x + -------
           ___
       2*\/ x

$$- 6 x + \frac{13}{2 \sqrt{x}}$$

Simplify

The second derivative [src]

 /      13  \
-|6 + ------|
 |       3/2|
 \    4*x   /

$$- (6 + \frac{13}{4 x^{\frac{3}{2}}})$$

Simplify

The third derivative [src]

  39  
------
   5/2
8*x

$$\frac{39}{8 x^{\frac{5}{2}}}$$

Simplify