What is the derivative of y tan x?

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To find the derivative of the function y tan x with respect to x, we need to apply the product rule of differentiation. The product rule states that if you have a function that is the product of two functions, say u and v, the derivative is given by:

  (uv)' = u'v + uv'

In our case, we can let:

  • u = y
  • v = tan x

We now need to compute the derivatives of u and v:

  • u’ = dy/dx (the derivative of y with respect to x)
  • v’ = sec2x (the derivative of tan x with respect to x)

Now we can apply the product rule:

  (y tan x)' = (dy/dx) tan x + y (sec2x)

Thus, the derivative of y tan x with respect to x is:

  dy/dx tan x + y sec2x

In summary, if y is a function of x, the derivative of the function y tan x is dy/dx tan x + y sec2x.

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