Questions: Find (f''(x)). (f(x)=(x^2+4)^6) (f''(x)=)

Find (f''(x)). (f(x)=(x^2+4)^6) (f''(x)=)
Transcript text: Find $f^{\prime \prime}(x)$. \[ f(x)=\left(x^{2}+4\right)^{6} \] \[ f^{\prime \prime}(x)= \]
failed

Solution

failed
failed

Solution Steps

Step 1: Find the First Derivative

To find the first derivative f′(x) f^{\prime}(x) of the function f(x)=(x2+4)6 f(x) = (x^2 + 4)^6 , we apply the chain rule. The result is: f′(x)=12x(x2+4)5 f^{\prime}(x) = 12x(x^2 + 4)^5

Step 2: Find the Second Derivative

Next, we differentiate the first derivative f′(x) f^{\prime}(x) to obtain the second derivative f′′(x) f^{\prime \prime}(x) . The calculation yields: f′′(x)=120x2(x2+4)4+12(x2+4)5 f^{\prime \prime}(x) = 120x^2(x^2 + 4)^4 + 12(x^2 + 4)^5

Final Answer

Thus, the second derivative of the function is: f′′(x)=120x2(x2+4)4+12(x2+4)5 \boxed{f^{\prime \prime}(x) = 120x^2(x^2 + 4)^4 + 12(x^2 + 4)^5}

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
3. 4. What type of storage media can be used to create a Windows system image? (Choose all that apply.) 5. a. DVDs b. Internal hard drive 6. c. External hard drive 7. d. Network drive
failedAnswered
In the last decade, 63% of climbers have successfully climbed Mt. Everest on their first attempt. This year about 300 first-time climbers will attempt to climb the summit. Use the normal approximation along with complete the climb on their first attempt. - Let X be the number of climbers out of 300 that will successfully complete the climb. Describe the distribution of X and its parameters: - Use the random variable notation to symbolically express the probability that at least 183 first-time climbers will successfully complete the climb: - Let Y be a normal variable that will be used to approximate the probability in question. Find the parameters of Y (round the answers to 2 decimal places): - Use the random variable notation to symbolically express the approximate probability that at least 183 climbers will successfully complete the climb: - Use the correction for continuity: - Find the probability (round the answer to 4 decimal places):
failedAnswered
Classify the species as Arrhenius bases, Bronsted-Lowry bases, or Lewis bases in aqueous solution. It is possible for a base to be of more than one type. Which species are Arrhenius bases? NaOH(aq) NH3 (aq) Br^-(aq) Which species are Bronsted-Lowry bases? NaOH(aq) Br^-(aq) NH3(aq)
failedAnswered
Graph the function. f(x)=-(x-3)^2 Choose the correct graph on the right. A. C. B. D.
failedAnswered
In the nervous system, which of the following is true of neurons and the neurotransmitters they secrete? Most neurons secrete many neurotransmitters at the same time. At any given time, a neuron is receiving a mixture of messages from the neurotransmitters. Neurotransmitters are located in the nuclei of the neurons. Neurotransmitters in neurons cannot be both excitatory and inhibitory.