Math CentralQuandaries & Queries


Subject: Derivatives
Name: Jacob
Who are you: Student

Find the derivative of: y= pi^2+x^2+3xy+sin(y^2)

Hi Jacob,

Without further explanation I will assume you want dy/dx and that y is a function of x. Look at the individual terms.

  • First pi is a constant, about 3.14, so pi2 is also a constant and hence its derivative is zero.

  • x2 is easy to differentiate.

  • 3xy is 3x times some function of x that you don't know. If you knew y, say y = cos(x), then you could differentiate 3xy, since it would be 3x cos(x). The derivative, using the product rule, would be
    d(3x cos(x))/dx = 3x d(cos(x))/dx + 3 cos(x).
    Using the same logic
    d(3xy) = 3x dy/dx + 3 y

  • The procedure here is similar to the previous term. Using the chain rule
    d(sin(y2)/dx = cos(y2) d(y2)/dx

Apply the chain rule again to find d(y2)/dx.

I hope this helps,

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