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y=sqrt(x)+4x^3−6

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Identical expressions
y=sqrt(x)+4x^ three − six
y equally square root of (x) plus 4x cubed −6
y equally square root of (x) plus 4x to the power of three − six
y=√(x)+4x^3−6
y=sqrt(x)+4x3−6
y=sqrtx+4x3−6
y=sqrt(x)+4x³−6
y=sqrt(x)+4x to the power of 3−6
y=sqrtx+4x^3−6
Similar expressions
y=sqrt(x)-4x^3−6

The derivative of the function/ y=sqrt(x)+4x^3−6

Derivative of y=sqrt(x)+4x^3−6

The solution

You have entered [src]

  ___      3    
\/ x  + 4*x  - 6

\left(\sqrt{x} + 4 x^{3}\right) - 6

sqrt(x) + 4*x^3 - 6

Detail solution

Differentiate $\left(\sqrt{x} + 4 x^{3}\right) - 6$ term by term:
1. Differentiate $\sqrt{x} + 4 x^{3}$ term by term:
  1. Apply the power rule: $\sqrt{x}$ goes to $\frac{1}{2 \sqrt{x}}$
  2. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
    So, the result is: $12 x^{2}$
  The result is: $12 x^{2} + \frac{1}{2 \sqrt{x}}$
2. The derivative of the constant $-6$ is zero.
The result is: $12 x^{2} + \frac{1}{2 \sqrt{x}}$

The answer is:

12 x^{2} + \frac{1}{2 \sqrt{x}}

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   1          2
------- + 12*x 
    ___        
2*\/ x

12 x^{2} + \frac{1}{2 \sqrt{x}}

Simplify

The second derivative [src]

         1   
24*x - ------
          3/2
       4*x

24 x - \frac{1}{4 x^{\frac{3}{2}}}

Simplify

The third derivative [src]

  /      1   \
3*|8 + ------|
  |       5/2|
  \    8*x   /

3 \left(8 + \frac{1}{8 x^{\frac{5}{2}}}\right)

Simplify

The graph

Derivative of y=sqrt(x)+4x^3−6