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y=x^3*log2x

Derivative of y=x^3*log2x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
 3         
x *log(2*x)
$$x^{3} \log{\left(2 x \right)}$$
d / 3         \
--\x *log(2*x)/
dx             
$$\frac{d}{d x} x^{3} \log{\left(2 x \right)}$$
Detail solution
  1. Apply the product rule:

    ; to find :

    1. Apply the power rule: goes to

    ; to find :

    1. Let .

    2. The derivative of is .

    3. Then, apply the chain rule. Multiply by :

      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:

      The result of the chain rule is:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
 2      2         
x  + 3*x *log(2*x)
$$3 x^{2} \log{\left(2 x \right)} + x^{2}$$
The second derivative [src]
x*(5 + 6*log(2*x))
$$x \left(6 \log{\left(2 x \right)} + 5\right)$$
The third derivative [src]
11 + 6*log(2*x)
$$6 \log{\left(2 x \right)} + 11$$
The graph
Derivative of y=x^3*log2x