**Introduction to derivative machine:**

Now a day the world widely depends on machines. The machines are work mush faster than human. They perform the operation with in a second. In mathematics, we also use the different machines for solving the problems. In mathematics machines are also known as calculator. There are different types of calculators are used in mathematics. They are derivative machine calculator, integrator machine calculator, and quadratic calculator.

**Derivative machine problem 1:**

Find the first order derivative value of the given function g(x) = 72x^{2} + 43x^{3} - 21x + 5

**Solution:**

Given function is g(x) = 72x^{2} + 43x^{3} - 21x + 5

Differentiate the given function with respect to x, we get

g'(x) = (72 * 2)x + (43 * 3)x^{2} - (21 * 1) + 0

= 144x + 129x^{2} - 21

**Answer:**

The final answer is 129x^{2} + 144x - 21

**Derivative machine problem 2:**

Find the second order derivative value of the given function g(x) = 15x^{4} + 32x^{3} - 10x^{2} + 3x

**Solution:**

Given function is g(x) = 15x^{4} + 32x^{3} - 10x^{2} + 3x

Differentiate the given function with respect to x, we get

g'(x) = (15 * 4)x^{3} + (32 * 3)x^{2} - (10 * 2)x + 3

= 60x^{3} + 96x^{2} - 20x

For finding second order derivative, differentiate g'(x) with respect to x, we get

g''(x) = (60 * 3)x^{2} + (96 * 2)x - 20

= 180x^{2} + 192x - 20

**Answer:**

The final answer is 180x^{2} + 192x - 20

**Derivative machine problem 3:**

Find the Second order derivative value of the given function u(x) = 8x^{3} + 20x^{2} - 16x + 46

**Solution:**

Given function is g(x) = 8x^{3} + 20x^{2} - 16x + 46

Differentiate the given function with respect to x, we get

g'(x) = (8 * 3)x^{2} + (20 * 2)x - (16 * 1) + 0

= 24x^{2} + 40x - 16

For finding second order derivative, differentiate g'(x) with respect to x, we get

g''(x) = (24 * 2)x + (40 * 1) - 0

= 48x + 40

**Answer:**

The final answer is 48x + 40

**Derivative machine problem 1:**

Differentiate the given function f(x) = 4x + 72x^{2}. Find the first order value of f(x).

**Answer:**

The final answer is f'(x) = 144x + 4

**Derivative machine problem 2:**

Differentiate the given function f(x) = 19x^{3}+ 41x^{2} + 20x. Find the first order value of f(x).

**Answer:**

The final answer is f'(x) = 57x^{2} + 82x + 20