Answer to Question #306092 in Calculus for Pearl

Question

a) Find 𝑑𝑦

𝑑𝑥

𝑔𝑖𝑣𝑒𝑛 𝑡ℎ𝑎𝑡 𝑦 = (𝑥

2 – 3x + 1)4

b) Differentiate 2

𝑥(x)−3𝑥+1

c) Intergrate 2x2 2

Answer 1

a) $y=(x^2-3x+1)4$

we start by simplifying the equation

$y=4x^2-12x+4$

we apply the sum/difference rule

$dy/dx =$ $d/dx(4x^2)-d/dx(12x)+d/dx(4)$

$=8x-12$

b. $y= 2x(x) -3(x)+1$

we start by simplifying the equation

$y=2x^2-3x+1$

to find the derivative we use sum difference rule

$dy/dx= d/dx(2x^2)-d/dx(3x)+d/dx(1)$

$=4x-3$

c. Incase the given equation is as follows

$\int( 2x^2+2)dx$

we apply the sum rule of integration

$=\int2x^2dx+\int2dx$

$=2x^3/3+2x+C$

where C is the constant of integration.

Incase the given equation is as follows

= $\int (2x^2-2)dx$

we apply the difference rule of integration

$=\int2x^2dx-\int 2dx$

where C is the constant of integration.