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Derivative of:
Derivative of y=x^4sin2x
Derivative of y=ln(x)*(2x^3)
Derivative of x^2+2
Derivative of sin(2x+3)
Identical expressions
y=ln(x)*(2x^ three)
y equally ln(x) multiply by (2x cubed )
y equally ln(x) multiply by (2x to the power of three)
y=ln(x)*(2x3)
y=lnx*2x3
y=ln(x)*(2x³)
y=ln(x)*(2x to the power of 3)
y=ln(x)(2x^3)
y=ln(x)(2x3)
y=lnx2x3
y=lnx2x^3

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

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

The solution

You have entered [src]

          3
log(x)*2*x

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

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

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

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:
  
  $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
  
  $f{\left(x \right)} = x^{3}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
  1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
  $g{\left(x \right)} = \log{\left(x \right)}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
  1. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
  The result is: $3 x^{2} \log{\left(x \right)} + x^{2}$
So, the result is: $6 x^{2} \log{\left(x \right)} + 2 x^{2}$
Now simplify:

$x^{2} \cdot \left(6 \log{\left(x \right)} + 2\right)$

The answer is:

$x^{2} \cdot \left(6 \log{\left(x \right)} + 2\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   2      2       
2*x  + 6*x *log(x)

$$6 x^{2} \log{\left(x \right)} + 2 x^{2}$$

Simplify

The second derivative [src]

2*x*(5 + 6*log(x))

$$2 x \left(6 \log{\left(x \right)} + 5\right)$$

Simplify

The third derivative [src]

2*(11 + 6*log(x))

$$2 \cdot \left(6 \log{\left(x \right)} + 11\right)$$

Simplify

The graph

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