If y = sec(u), dy/dx equals?

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Multiple Choice

If y = sec(u), dy/dx equals?

Explanation:
The derivative is found by applying the chain rule to a composite function. The derivative of sec(s) with respect to its argument s is sec(s) tan(s). With y = sec(u(x)), dy/dx = sec(u) tan(u) · du/dx. Since du/dx is u', this becomes dy/dx = u' sec(u) tan(u). This matches the given answer because the outer function sec(u) contributes sec(u) tan(u) and the inner function u(x) contributes its derivative u'. The other forms would arise from differentiating a different trig function or introducing a negative sign, which does not apply here for sec.

The derivative is found by applying the chain rule to a composite function. The derivative of sec(s) with respect to its argument s is sec(s) tan(s). With y = sec(u(x)), dy/dx = sec(u) tan(u) · du/dx. Since du/dx is u', this becomes dy/dx = u' sec(u) tan(u). This matches the given answer because the outer function sec(u) contributes sec(u) tan(u) and the inner function u(x) contributes its derivative u'. The other forms would arise from differentiating a different trig function or introducing a negative sign, which does not apply here for sec.

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