Find d^2y/dx^2 if 5x^3 - y^3 = 25 A. -250x/y^5

B. (10x(y^2-x))/y^3

C. 5x^2/y^2

D. (10(y^2-5x^4))/y^3

E. 30x - 6y

Choice A.

Step-by-step explanation:

We are given:

We are asked to find:

This requires we first find:

Let's begin.

We will differentiate the right hand side using the constant rule since 25 is just a constant. We will differentiate the left hand side using difference rule  and then constant multiple rule and then power rule and chain rule.

Now let's solve for .

Add on both sides:

Divide both sides by :

Symmetric property of equality:

Simplify right hand side:

Now let's find the second derivative by differentiating both sides of this equation. We will use the quotient rule on the right hand side:

We can replace with ... since we just got this result before differentiating both sides of an equality again.

So we have:

Let's simplify the 2nd term on top by cancelling a common factor of y in that term from top and bottom:

We still don't like having this compound fraction (a mini fraction inside a bigger fraction). Let's get rid of that...Multiply numerator and denominator by for the big fraction to clear the mini fraction out.

Distribute:

Simplifying a bit more:

We could factor the top a bit... both terms on top of a common factor of :

Notice the thing in ( ) on top is the exact opposite of the left hand side of our original equation: .

This implies we can replace it with -25:

step-by-step explanation:

de-gf

hj=3x+20

ji=15x-64