X - 13 = 5x + 7 a) -5 b) 3 c) 6 d) 2

Mathematics

1 answer:

Alex4 years ago

6 0

$x-13=5x+7\ \ \ \ |+13\\\\x=5x+20\ \ \ \ |-5x\\\\-4x=20\ \ \ \ |:(-4)\\\\x=-5\\\\Answer:\ a)\ -5$

You might be interested in

How would i approximate each irrational square root number to the nearest 0.05? 34, 82, 45, 104, -71, and -19

Digiron [165]

Using a calculator or a pencil, find each square root, including
three (3) decimal places. A negative number has no real square
roots, so skip '-71' and '-19'.

For each square root . . .

-- If the digits in the 2nd and 3rd decimal place are 00 through 24, then
make the 2nd decimal place a '0' and discard the rest.

-- If the digits in the 2nd and 3rd decimal place are 25 through 74, then
make the 2nd decimal place a '5' and discard the rest.

-- If the digits in the 2nd and 3rd decimal place are 75 through 99, then
increase the 1st decimal place by 1, make the 2nd decimal place a '0',
and discard the rest.

4 0

4 years ago

If f(x) = 9x10 tan−1x, find f '(x).

djverab [1.8K]

Answer:

$\displaystyle f'(x) = 90x^9 \tan^{-1}(x) + \frac{9x^{10}}{x^2 + 1}$

General Formulas and Concepts:

Calculus

Differentiation

Derivatives
Derivative Notation

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

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Product Rule]: $\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle f(x) = 9x^{10} \tan^{-1}(x)$

Step 2: Differentiate

[Function] Derivative Rule [Product Rule]: $\displaystyle f'(x) = \frac{d}{dx}[9x^{10}] \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]$
Rewrite [Derivative Property - Multiplied Constant]: $\displaystyle f'(x) = 9 \frac{d}{dx}[x^{10}] \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]$
Basic Power Rule: $\displaystyle f'(x) = 90x^9 \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]$
Arctrig Derivative: $\displaystyle f'(x) = 90x^9 \tan^{-1}(x) + \frac{9x^{10}}{x^2 + 1}$