What is the domain of sqrt 3x-3?
2 answers:
For this case we must find the domain of the following expression:
The domain will be given by all the values for which the function is defined. For the given expression to be defined, the argument of the root must be positive. That is to say:
Thus, the domain will be given by all the numbers greater than or equal to 1.
Answer:
Domain:
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You can actually use either the product rule or the chain rule for this one. Observe:
• Method I:
y = cos² x
y = cos x · cos x
Differentiate it by applying the product rule:
The derivative of cos x is – sin x. So you have
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• Method II:
You can also treat y as a composite function:
and then, differentiate y by applying the chain rule:
For that first derivative with respect to u, just use the power rule, then you have
and then you get the same answer:
I hope this helps. =)
Tags: <em>derivative chain rule product rule composite function trigonometric trig squared cosine cos differential integral calculus</em>
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You can actually use either the product rule or the chain rule for this one. Observe:
• Method I:
y = cos² x
y = cos x · cos x
Differentiate it by applying the product rule:
The derivative of cos x is – sin x. So you have
—————
• Method II:
You can also treat y as a composite function:
and then, differentiate y by applying the chain rule:
For that first derivative with respect to u, just use the power rule, then you have
and then you get the same answer:
I hope this helps. =)
Tags: <em>derivative chain rule product rule composite function trigonometric trig squared cosine cos differential integral calculus</em>