Help ASAP with this question

3√x -2/x^2<br><br>please show step by step of differentiation before combining the terms.

EastWind [94]

Answer:

Step-by-step explanation:

Before we differentiate, let us assign a variable to the function. Let y be equal to the function i.e let y = 3√x -2/x²

In differentiation if $y = ax^{n}$ , then $\frac{dy}{dx} = nax^{n-1}$ where n is a constant and dy/dx means we are differentiating the function y with respect to x.

Applying the formula o the question given;

$y= 3\sqrt{x} -2/x^2\\y = 3{x}^\frac{1}{2} - 2x^{-2} \\\\$

On differentiating the resulting function;

$\frac{dy}{dx} = \frac{1}{2}*3x^{\frac{1}{2}-1 } - (-2)x^{-2-1} \\\\\frac{dy}{dx} = \frac{1}{2}*3x^{-\frac{1}{2}} + 2x^{-3}\\ \\\frac{dy}{dx} = \frac{1}{2}*{\frac{3}{x^{\frac{1}{2} } }} + \frac{2}{x^{3} } \\\\\frac{dy}{dx} = {\frac{3}{2x^{\frac{1}{2} } }} + \frac{2}{x^{3} }\\\\\frac{dy}{dx} = {\frac{3}{2\sqrt{x} }} + \frac{2}{x^{3} }$

To combine the terms, we will add up by finding their LCM.

$\frac{dy}{dx} = {\frac{3}{2\sqrt{x} }} + \frac{2}{x^{3} }\\\frac{dy}{dx} = \frac{3x^3+4\sqrt{x} }{2x^{3} \sqrt{x}}$

3 0

4 years ago

(2 12)-3 6)parethesis two plus twelve parethesis subtraction three plus six

ira [324]

You should use Order of Operations or PEDMAS for this (Parenthesis, Exponents, Division and Multiplication in the order they appear, Addition and Subtraction in the order they appear). So we do the 2+12 because that is in parentheses first which gives 14-3+6. Next we do 14-3 because there are no exponents and no division or multiplication, which gives 11+6. This yields your answer, 17.

8 0

3 years ago

Can anyone give me a few reasons why school cafeteria food is bad

Furkat [3]

Answer:

its bad because its microwaved

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Determine the equivalent system for the given system of equations.<br> 4x - 5y = 2<br> 3x - y = 8

Black_prince [1.1K]

Solving the system of equations we get solution set (38/11,26/11)

Step-by-step explanation:

We need to solve the system of equations:

$4x - 5y = 2\\3x - y = 8$

Let:

$4x - 5y = 2\,\,\,eq(1)\\3x - y = 8\,\,\,eq(2)$

Multiply equation 2 with 5 and subtract both equations to find value of x:

$4x - 5y = 2\\15x - 5y = 40\\-\,\,\,\,+\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,-\\--------\\-11x=-38\\x=\frac{-38}{-11}\\x=\frac{38}{11}$

So, value of x = 38/11

Now, finding y:

Putting value of x in equation 2

$3x-y=8\\3(\frac{38}{11})-y=8\\\frac{114}{11}-y=8\\-y=8-\frac{114}{11}\\-y=\frac{8*11-114}{11}\\-y=\frac{88-114}{11}\\-y=\frac{-26}{11}\\y=\frac{26}{11}$

So, value of y = 26/11

So, Solving the system of equations we get solution set (38/11,26/11)

Keywords: System of equations

Learn more about system of equations at:

#learnwithBrainly

6 0

3 years ago

9q - 32 = 67, what is the value of q?

elixir [45]

Alright, if you do the math, then it goes out to q=11.

7 0

3 years ago

Read 2 more answers