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Derivative of:
Derivative of 5*x^2-2/sqrt(x)+sin(pi/4)
Derivative of 1/3*x^3
Derivative of x^2/(x^2+1)
Derivative of x*sqrt(3-x)
Identical expressions
y=x^ three *log(two)*x
y equally x cubed multiply by logarithm of (2) multiply by x
y equally x to the power of three multiply by logarithm of (two) multiply by x
y=x3*log(2)*x
y=x3*log2*x
y=x³*log(2)*x
y=x to the power of 3*log(2)*x
y=x^3log(2)x
y=x3log(2)x
y=x3log2x
y=x^3log2x

The derivative of the function/ y=x^3*log(2)*x

Derivative of y=x^3log(2)x

The solution

You have entered [src]

 3         
x *log(2)*x

$$x x^{3} \log{\left(2 \right)}$$

d / 3         \
--\x *log(2)*x/
dx

$$\frac{d}{d x} x x^{3} \log{\left(2 \right)}$$

Transform

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Apply the product rule:
  
  $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
  
  $f{\left(x \right)} = x$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
  1. Apply the power rule: $x$ goes to $1$
  $g{\left(x \right)} = x^{3}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
  1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
  The result is: $4 x^{3}$
So, the result is: $4 x^{3} \log{\left(2 \right)}$

The answer is:

$4 x^{3} \log{\left(2 \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   3       
4*x *log(2)

$$4 x^{3} \log{\left(2 \right)}$$

Simplify

The second derivative [src]

    2       
12*x *log(2)

$$12 x^{2} \log{\left(2 \right)}$$

Simplify

The third derivative [src]

24*x*log(2)

$$24 x \log{\left(2 \right)}$$

Simplify

The graph

Derivative of y=x^3*log(2)*x