Differentiate y = x^2 e^{2x}, = x^2 ln(x), = sin(x)/x, = sqrt[x]/cos(x), = 2 sin(...

[MathTy]

a) Differentiate the following products with respect to x.

. . .\(\displaystyle \mbox{i. }\, y\, =\, x^2\, e^{2x}\)

. . .\(\displaystyle \mbox{ii. }\, y\, =\, x^2\, \ln(x)\)

b) Differentiate the following quotients with respect to x.

. . .\(\displaystyle \mbox{i. }\, y\, =\, \dfrac{\sin(x)}{x}\)

. . .\(\displaystyle \mbox{ii. }\, y\, =\, \dfrac{\sqrt{x\,}}{\cos(x)}\)

c) Differentiate the following function of a function with respect to x.

. . .\(\displaystyle \mbox{i. }\, y\, =\, 2\, \sin(3x\, -\, 2)\)

. . .\(\displaystyle \mbox{ii. }\, y\, =\, 2\, \cos^5(x)\)

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If someone would be able to help me with these calculus questions and explain your answers that would be great (these are questions from an examination past paper) and i'd really like to get my head around them.
Thanks

 

[tkhunny]

a) Differentiate the following products with respect to x.

. . .\(\displaystyle \mbox{i. }\, y\, =\, x^2\, e^{2x}\)

. . .\(\displaystyle \mbox{ii. }\, y\, =\, x^2\, \ln(x)\)

b) Differentiate the following quotients with respect to x.

. . .\(\displaystyle \mbox{i. }\, y\, =\, \dfrac{\sin(x)}{x}\)

. . .\(\displaystyle \mbox{ii. }\, y\, =\, \dfrac{\sqrt{x\,}}{\cos(x)}\)

c) Differentiate the following function of a function with respect to x.

. . .\(\displaystyle \mbox{i. }\, y\, =\, 2\, \sin(3x\, -\, 2)\)

. . .\(\displaystyle \mbox{ii. }\, y\, =\, 2\, \cos^5(x)\)

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If someone would be able to help me with these calculus questions and explain your answers that would be great (these are questions from an examination past paper) and i'd really like to get my head around them.

a. Use the Product Rule
b. Use the Quotient Rule.
c. Use the Chain Rule.

These are fundamental principles.

 

[MathTy]

a. Use the Product Rule
b. Use the Quotient Rule.
c. Use the Chain Rule.

These are fundamental principles.

Would you be able to help me out a bit? I’m a complete beginner and just doing these past papers to increase my knowledge of calculus as an engineer


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[Dr.Peterson]

Would you be able to help me out a bit? I’m a complete beginner and just doing these past papers to increase my knowledge of calculus as an engineer


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If your goal is to increase your ability to do these things, then it is essential that you practice doing them. If you just don't understand the rules at all, say so and we can either direct you to a source of teaching on them, or give you some examples. Otherwise, make some attempt at applying the rules to these problems, so we can see specifically where you are struggling, and help you along.

If you are really a complete beginner, perhaps you should be starting with some easier problems, showing your work on those so we can make sure you have the necessary foundation for the hard ones.

 

[sinx]

Would you be able to help me out a bit? I’m a complete beginner and just doing these past papers to increase my knowledge of calculus as an engineer
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i am a bit confused.
you cannot be an engineer without being able to use calculus (really well).
so being both an engineer and a complete beginner in calculus does not make sense.

If your goal is to learn to use calculus to solve engineering problems;
My answer is you need to buy a good book and start at the beginning.
then after you have attempted to work the problems, post whatever questions you may have.

 

[Steven G]

View attachment 9258
If someone would be able to help me with these calculus questions and explain your answers that would be great (these are questions from an examination past paper) and i'd really like to get my head around them.
Thanks

tkhunny gave you the needed hints. Let's work with the 1st one. Do you know the product rule? If not, then of course you can't do these. Respond back to the rule for taking derivatives of a product. Even try to use this rule. Then someone will help you.