Find the derivative of f(x)= e^(4x) + e^-(4x)

Mathematics

2 answers:

ololo11 [35]3 years ago

4 0

Answer:

$f'(x)=4e^{4x} -4e^{-4x}$

Step-by-step explanation:

To find this derivative, we will need to use the chain rule.

As there is a variable in the exponent we can use this formula:

$f'(x)=u'e^u$

In this case, $u=4x$ and $u=-4x$

This means that $u'=4$ and $u'=-4$ respectively

This gives us $f'(x)=4e^{4x} -4e^{-4x}$

xeze [42]3 years ago

4 0

Answer:

Step-by-step explanation:

note : (e^(u(x))' = (u(x))'e^(u(x)

f(x)= e^(4x) + e^-(4x)

f'(x) =4e^(4x) - 4 e^-(4x)

You might be interested in

The price of a laptop is $420. The price of a phone is 35% of the price of this laptop. What is the price of the phone? A $12 B

Pavel [41]

The correct answer would be B. $420x0.35=$147.00

8 0

3 years ago

Read 2 more answers

Suppose a continuous probability distribution has an average of μ=35 and a standard deviation of σ=16. Draw 100 times at random

yulyashka [42]

Answer:

To use a Normal distribution to approximate the chance the sum total will be between 3000 and 4000 (inclusive), we use the area from a lower bound of 3000 to an upper bound of 4000 under a Normal curve with its center (average) at 3500 and a spread (standard deviation) of 160 . The estimated probability is 99.82%.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .