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Differentiate the functions ( calculus ) watch

1. HELP!!!!!!!!!!!!!!!!!!!!!!!!!!! ASAP terrible at this calculus

Differentiate the functions
1. y=5x^2 ln(3x)
2. y=4sin(5x) over 5x^4
3. y=(4+2x)^6
2. (Original post by hugani)
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!! ASAP terrible at this calculus

Differentiate the functions
1. y=5x^2 ln(3x)
2. y=4sin(5x) over 5x^4
3. y=(4+2x)^6
Do you understand the product rule and quotient rule and the chain rule? they are essential to understanding these and once you lay it out in those formulas it is never so bad.

1. Product rule (u'v + v'u) can be written as (5x^2)(ln3x)

2. You can do either the quotient rule or the product rule here.
Quotient rule (u'v - v'u)/v^2 although I prefer to write the equation as (4sin5x)(5x^4)^-1 and use the product rule above.

3. Chain rule treat this as the chain rule (you have an inner function, which can be expressed generally as f(g(x))). The chain rule is f'(g(x))g'(x) or more comely written as dy/dx = dy/dt x dt/dx

inside each of these you have other nested functions. Such as the sin and log function nested inside the main function you are trying to differentiate, when it comes to parts of the formula when you need to differentiate these functions, use the chain rule as you have a function nested in a function (sin3x) is f(g(x)) where f(x) is the sine function and g(x) is 3x.

If you need actual step by step help for each question feel free to ask and i'll help run you through them, but hopefully this should be enough for you to takle them on your own

3. 1. Using the product rule...
Let u = 5x^2 U' = 10x
V = ln(3x) v' = 1/x
Therefore... dy/dx = 5x^2*1/x + 10x*ln(3x)
Dy/dx = 5x + 10xln(3x)

2. Using the quotient rule...
Let u = 4sin(5x) u' = 20cos(5x)
V = 5x^4 V' = 20x^3
Dy/dx = (100x^4*cos(5x) - 80x^3*sin(5x))/25x^8)
Dy/dx = (20xcos(5x) - 16sin(5x))/5x^5

3. Using the chain rule...
Y = 2^6(2+x)^6
Dy/dx = 384(2+x)^5
4. (Original post by Hdvhju)
1. Using the product rule...

...
Please don't post full solutions - it's against forum rules!

Thanks

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Updated: January 10, 2017
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