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By differentiating with respect to x, 3x^2+6x(dy/dx)+6y+2y(dy/dx)=0 So, dy/dx(6x+2y)=-3x^2-6y so dy/dx = -(3x^2+6y)/(2(3x+y))

Imagine the function f(x) as a black box which takes in any value x and produces an output y. The black box acts on its input according to a rule which produces a unique value of y for a given x. If the b...

First set up integral. Do not forget dx!

Int(f(x)) between 0 and 1

Optionally take out factor of 3 to simplify problem.

Solve using substitution and the exponential rule.

Integ...

Multiply the first term in the first bracket, so that would be x, with the second bracket. step one: x(x-3) is identical to: x^2 - 3x

We can now multiply the second number in the first bracket, whi...

y = 4x^3 - 5/x^2 Easier to differentiate the 2nd term if it isn't written as a fraction so first rewrite y: y = 4x^3 - 5x^(-2) Then differentiate each term by multiplying each term by the current power of...