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log(5)*(3*x+1)^10
The derivative of the function/ log(5)*(3*x+1)^10

Derivative of log(5)*(3*x+1)^10

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
                10
log(5)*(3*x + 1)
$$\left(3 x + 1\right)^{10} \log{\left(5 \right)}$$ 
d /                10\
--\log(5)*(3*x + 1)  /
dx
$$\frac{d}{d x} \left(3 x + 1\right)^{10} \log{\left(5 \right)}$$
Transform
Detail solution

  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. Let .

    2. Apply the power rule: goes to

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

      1. Differentiate 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: goes to

          So, the result is:

        2. The derivative of the constant is zero.

        The result is:

      The result of the chain rule is:

    So, the result is:

  2. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
            9       
30*(3*x + 1) *log(5)
$$30 \left(3 x + 1\right)^{9} \log{\left(5 \right)}$$
Simplify
The second derivative [src] 
             8       
810*(1 + 3*x) *log(5)
$$810 \left(3 x + 1\right)^{8} \log{\left(5 \right)}$$
Simplify
The third derivative [src] 
               7       
19440*(1 + 3*x) *log(5)
$$19440 \left(3 x + 1\right)^{7} \log{\left(5 \right)}$$
Simplify
The graph
Derivative of log(5)*(3*x+1)^10
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