calc review (derivatives)

[paulxzt]

So I have some problems from day 1 calc that I need some help on:

Find dy/dx for xy=3x^2 + 5y
can someone tell me if 6x / x - 5 is correct?

Find dy/dx for y = sin^3(4x)
Please help on how to get it started. Do I do 3cox^2(4x)(4) ?

Find dy/dx for y = 5x^2tan(3x)
What rule would I use? Would I begin by writing 10xtan3x then proceed with mult. rule?

Any help is appreciated. Thanks.

 

[galactus]

So I have some problems from day 1 calc that I need some help on:

Find dy/dx for xy=3x^2 + 5y
can someone tell me if 6x / x - 5 is correct?.

\(\displaystyle \L\\xy-3x^{2}-5y=0\)

\(\displaystyle \L\\x\frac{dy}{dx}+y-6x-5\frac{dy}{dx}=0\)

\(\displaystyle \L\\\frac{dy}{dx}=\frac{6x-y}{x-5}\)

 

[skeeter]

So I have some problems from day 1 calc that I need some help on:

Find dy/dx for xy=3x^2 + 5y
can someone tell me if 6x / x - 5 is correct?

Find dy/dx for y = sin^3(4x)
Please help on how to get it started. Do I do 3cox^2(4x)(4) ?

know the chain rule?
y = [sin(4x)]³
dy/dx = 3[sin(4x)]²*cos(4x)*4 = 12sin²(4x)cos(4x)


Find dy/dx for y = 5x^2tan(3x)
What rule would I use? Would I begin by writing 10xtan3x then proceed with mult. rule?

product rule and chain rule ...
y = 5x²tan(3x)
dy/dx = 5x²sec²(3x)*3 + tan(3x)*10x
dy/dx = 15x²sec²(3x) + 10x*tan(3x)


Any help is appreciated. Thanks.