Mister Exam

Derivative of y=(3x-1)(2x+5)

Function f() - derivative -N order at the point
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The graph:

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Piecewise:

The solution

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(3*x - 1)*(2*x + 5)
(2x+5)(3x1)\left(2 x + 5\right) \left(3 x - 1\right)
(3*x - 1)*(2*x + 5)
Detail solution
  1. Apply the product rule:

    ddxf(x)g(x)=f(x)ddxg(x)+g(x)ddxf(x)\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(x)=3x1f{\left(x \right)} = 3 x - 1; to find ddxf(x)\frac{d}{d x} f{\left(x \right)}:

    1. Differentiate 3x13 x - 1 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: xx goes to 11

        So, the result is: 33

      2. The derivative of the constant 1-1 is zero.

      The result is: 33

    g(x)=2x+5g{\left(x \right)} = 2 x + 5; to find ddxg(x)\frac{d}{d x} g{\left(x \right)}:

    1. Differentiate 2x+52 x + 5 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: xx goes to 11

        So, the result is: 22

      2. The derivative of the constant 55 is zero.

      The result is: 22

    The result is: 12x+1312 x + 13


The answer is:

12x+1312 x + 13

The graph
02468-8-6-4-2-1010-10001000
The first derivative [src]
13 + 12*x
12x+1312 x + 13
The second derivative [src]
12
1212
The third derivative [src]
0
00
The graph
Derivative of y=(3x-1)(2x+5)