Calculate dy/dx when y = (x2 + 2)e 4x as the derivative of a product, letting u = x2 + 2 and v = e4x . Which of the following is a step in your solution? A. dv/dx = 4xe3x
B. du/dx = 2x + 2
C. dv/dx = 4xe4x
D. du/dx = 2x


Answer 1


D. du/dx = 2x

Step-by-step explanation:

Given to find dy/dx where;

Then when you let;

u=x²+2    and


In  u=x²+2  du/dx = 2x------------------------step 1

In e^4x, dv/dx = e^4x * d/dx (4x)

=e^4x *4 = 4e^4x------------------------------------step 2

Related Questions


Evaluate cotθ if sinθ= √6/5


Answer: .

Step-by-step explanation: Given sinθ= √6/5.

We know radio of .



Let us apply Pythagoras Theorem to find the third side(Adjacent side) of the triangle .

Subtracting 6 from both sides, we get

Therefore, adjacent side =

We know,




An advisor to the mayor of a large city wants to estimate, within 3 minutes, the mean travel time to work for all employees who work within the city limits. He knows that the standard deviation for all travel times is 12.25 minutes. He also wants to achieve a 95% confidence interval. He will poll a random sample of city employees. At least how many employees should he poll?




Step-by-step explanation:

Given that an advisor to the mayor of a large city wants to estimate, within 3 minutes, the mean travel time to work for all employees who work within the city limits.

Let X be the random variable denoting the time for employees to travel within city limit

Std dev of X

For 95% confidence interval Z critical 1.96 is used because population std dev is known

Margin of error


where n is the desired sample size.

Simplify to get

Hence atleast 64 employees should he poll


A label covers the lateral surface area of a can. The can has a diameter of 2.6 inches and a height of 4 inches. What is the lateral surface area of the label?



First of all, lateral means the sides of the can in this case.

Calculate the surface area of the can, subtract the area of the top and bottom which are two circles, and theres the answer!

Step-by-step explanation:

1. SA= 2πrh+2πr^2

= 2(π)(1.3)(4) + 2(π)(1.3^2)

= 43.29- (π1.3^2)^2


Please note that ^(a number) means to the power of (that number). Hope this helps!



Step-by-step explanation:

Now we need the circumference of the circle, with the formula 2 pi r

2 times pi is about 6.28 that times the radius, (1.3) Which is 8.17.

So the circumference of the circle is 8.17, and the height is 4.  

Multiply those together to get the surface area around the can. Not including the top and bottom.

8.17 * 4 = 32.68

The surface area of the label of the can is 32.68


Which congruence theorem can be used to prove △ABR ≅ △ACR


The answer:
according to the figure, the sides of the two triangles △ABR and △ACR  have specific congruence. 
the congruences are:
AB≅ BC and AR ≅ CR, these mean that the sides are proportional

such triangles are called similar

so  to prove that △ABR ≅ △ACR , we can use SSS theorem
side-side -side Similarity theorem

HL - Hypotenuse Leg

SAS - Side Angle Side

SSS - Side Side Side

Random Questions
Will this happen in avenger 4? When one of Thanos's "children" was trying to take the Time Stone from Doctor Strange, Doctor Strange told him that there was a "simple, but powerful" curse on it. Doctor Strange must've taken the curse off to put the fake necklace on so Thanos couldn't forcefully rip it off later in their fight. I think that when he took the curse off the Stone, he had time to look back in time and tell Captain Marvel, and Nick Fury to get two of those transponders from the after-scene from Avengers Infinity War. He told Nick Fury to press the button when The Snap happened. And he told Captain Marvel to go into a part of the Quantum Realm where time was very slow so she would only have to wait a few hours or something, for years to pass. And when Captain Marvel's transponder went off she would leave the Quantum Realm, and save Ant-Man on her way out. Then she would blast off into space to save Tony Stark and Nebula, and go back to Earth. During all this, Captain America is making a plan. His plan is similar to Loki's plan when Loki attacked New York. Erik Salvig and Bruce Banner will work together to open a portal to the Space Stone. (Loki did just that. He was able to portal right into that Shield base, where the tesseract was, in the 1st Avengers movie.) Erik Salvig has had experiences with these types of things, like in a few of the Thor movies and when Loki brain-washed him so he could work with the tesseract. So if they find the space stone then they find Thanos. But they may need a powerful power source. Like how they were able to destroy the mind stone with Scarlet Witches’ powers. But Scarlet Witch is dead. So maybe when Captain Marvel gets back, she can use her powers to do something to help them. Then they can open up a portal to the Space Stone, which is where Thanos is. Then the can beat him up and take the Stones and fix everything.