   Chapter 2.4, Problem 9E

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# Differentiate. y = x 2 − tan x

To determine

To differentiate: the given function using differentiation rules.

Explanation

1) Concept:

y is division of two functions that is x and  (2-tanx). So to find the derivative of   y, use quotient rule and then use standard differentiation rule.

2) Formula:

i. Quotient rule:

ddxfxgx=gx*ddxfx-fx*ddx(gx)gx2

ii. Derivative of tangent:

ddxtanx=sec2x

3) Given:

y=x2-tanx

4) Calculations:

Using quotient rule:

dydx=2-tanx*ddxx-x*ddx(2-tanx)2-tanx2

Compute the derivatives using differentiation rules

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