5x (x - 4) = 0 Solve it in standard form

What is the derivative of 1/square root 4x.

Bumek [7]

Answer:

$\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{-1}{4x^\bigg{\frac{3}{2}}}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Exponential Properties

Exponential Property [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$
Exponential Property [Root Rewrite]: $\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}$

Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Derivative Rule [Basic Power Rule]:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

Step 1: Define

Identify.

$\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg]$

Step 2: Differentiate

Simplify: $\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \bigg( \frac{1}{2\sqrt{x}} \bigg)'$
Rewrite [Derivative Property - Multiplied Constant]: $\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{1}{2} \bigg( \frac{1}{\sqrt{x}} \bigg)'$
Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{1}{2} \bigg( \frac{1}{x^\Big{\frac{1}{2}}} \bigg)'$
Rewrite [Exponential Rule - Rewrite]: $\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{1}{2} \bigg( x^\bigg{\frac{-1}{2}} \bigg)'$
Derivative Rule [Basic Power Rule]: $\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{1}{2} \bigg( \frac{-1}{2} x^\bigg{\frac{-3}{2}} \bigg)$
Simplify: $\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{-1}{4} x^\bigg{\frac{-3}{2}}$
Rewrite [Exponential Rule - Rewrite]: $\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{-1}{4x^\bigg{\frac{3}{2}}}$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

5 0

3 years ago

Use picture above. Write the ratio. Please explain what the ratio means.

PIT_PIT [208]

1) 2:5 ratio

This is a fairly simple process, you count how many of each and then put them in order the way the question asks.

So there are 5 cans and 2 bottles. The question asks "bottles to cans" so the correct answer HAS to be 2:5, NOT 5:2.

2) 3:1

There is 1 spoon and 3 forks. The question asks "forks to spoons" so the correct answer HAS to be 3:1, NOT 1:3

7 0

4 years ago

Exact volume of this cylinder

never [62]

I am taking this quiz but I'm pretty sure its....c

6 0

3 years ago

Read 2 more answers

Jazzie runs 5 miles each day.How many days will it take her to jog 57 miles?

kodGreya [7K]

Answer:

It will take her 11.4 days, or 12 whole days to jog 57 miles

Step-by-step explanation:

1 day = 5 miles

? days = 57 miles

57/5 = 11.4 days

4 0

3 years ago

Read 2 more answers

WILL MARK BRANLIEST!!!!!Use the following net to find the volume of the solid figure it represents. 88 yd3 94 yd3 48 yd3 144 yd

Bad White [126]

We need to solve the net volume of the given problem and we have 6 total rectangles with areas. Solving for the volume we have:
Length = 6 yard
width = 4 yard
height = 2 yard
Solving for the volume, we have:
Volume = 6 x 4 x 2
Volume = 48 yard³

The answer is 48 yard³.

8 0

3 years ago

Read 2 more answers