Use the power, product, and chain rules:

• product rule

• power rule for the first term, and power/chain rules for the second term:

• power rule

Now simplify.

You could also use logarithmic differentiation, which involves taking logarithms of both sides and differentiating with the chain rule.
On the right side, the logarithm of a product can be expanded as a sum of logarithms. Then use other properties of logarithms to simplify

Differentiate both sides and you end up with the same derivative:

Answer:
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Step-by-step explanation:
Answer:

Step-by-step explanation:
Given


Required
Probability of not getting audited
If a pair of dice is rolled, the following are the observations of the sum




So, in a single roll; The probability of getting audited is:



The probability of not getting audited in a single roll is:
--- Complement rule

Take LCM


The probability of not getting audited in 5 rolls is:




<h3>Given</h3>
tan(x)²·sin(x) = tan(x)²
<h3>Find</h3>
x on the interval [0, 2π)
<h3>Solution</h3>
Subtract the right side and factor. Then make use of the zero-product rule.
... tan(x)²·sin(x) -tan(x)² = 0
... tan(x)²·(sin(x) -1) = 0
This is an indeterminate form at x = π/2 and undefined at x = 3π/2. We can resolve the indeterminate form by using an identity for tan(x)²:
... tan(x)² = sin(x)²/cos(x)² = sin(x)²/(1 -sin(x)²)
Then our equation becomes
... sin(x)²·(sin(x) -1)/((1 -sin(x))(1 +sin(x))) = 0
... -sin(x)²/(1 +sin(x)) = 0
Now, we know the only solutions are found where sin(x) = 0, at ...
... x ∈ {0, π}
Answer:
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Step-by-step explanation:
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