Show that cos 30 degree + sin 60 degree / 1+ sin 30 degree + cos 60 degree is equal to cos 30 degree

Mathematics

1 answer:

Soloha48 [4]2 years ago

5 0

Answer:

cos 30

Step-by-step explanation:

cos 30 + sin 60 / 1+ sin 30 + cos 60

= root3 / 2 + root3/2 / 1 + 1/2 + 1/2

= root 6/2 by 4/2

= root 6/4

= root 3/2

= cos 30

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Find f'(x) and state the domain of f': f(x) = In (2x^2+1)

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Answer:

$f'(x) = \frac{4x}{2x^2+1}$

Domain: All Real Numbers

General Formulas and Concepts:

Algebra I

Domain is the set of x-values that can be inputted into function f(x)

Calculus

The derivative of a constant is equal to 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Chain Rule: $\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Derivative: $\frac{d}{dx} [ln(u)] = \frac{u'}{u}$

Step-by-step explanation:

Step 1: Define

f(x) = ln(2x² + 1)

Step 2: Differentiate

Derivative ln(u) [Chain Rule/Basic Power]: $f'(x) = \frac{1}{2x^2+1} \cdot 2 \cdot 2x^{2-1}$
Simplify: $f'(x) = \frac{1}{2x^2+1} \cdot 4x$
Multiply: $f'(x) = \frac{4x}{2x^2+1}$

Step 3: Domain

We know that we would have issues in the denominator when we have a rational expression. However, we can see that the denominator would never equal 0.

Therefore, our domain would be all real numbers.

We can also graph the differential function to analyze the domain.