Ethan writes 2/3 of a page in 5/12 of a minute. How much time does it take him to write one page

1 answer:

8 0

2/3 of a page in 5/12 of a minute

Multiply both fractions by 3/2

$\frac{2}{3} \times \frac{3}{2} = 1$

$\frac{5}{12} \times \frac{3}{2} = \frac{5}{4} \times \frac{1}{2}=\frac{5}{8}$

So, Ethan can read 1 page in 5/8 of a minute.

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Differentiating a Logarithmic Function In Exercise, find the derivative of the function.

sp2606 [1]

Answer:

$\dfrac{d(f(x))}{dx} = \dfrac{2}{x}$

Step-by-step explanation:

We are given the following function in the question:

$f(x) = \ln (3x^2)$

We have to derivate the given function.

Formula:

$\dfrac{d(\ln x)}{dx} = \dfrac{1}{x}\\\\\dfrac{d(x^n)}{dx} = nx^{n-1}$

The derivation takes place in the following manner

$f(x) = \ln (3x^2)\\\\\dfrac{d(f(x))}{dx} = \displaystyle\frac{d(\ln(3x^2))}{dx}\\\\=\frac{1}{3x^2}\times \frac{d(3x^2)}{dx}\\\\= \frac{1}{3x^2}\times (6x)\\\\=\frac{6x}{3x^2}\\\\=\frac{2}{x}$