To determine

To find: The differentiation of y=x2−tanx.

Answer

The differentiation of y=x2−tanx is 2−tanx+xsec2x(2−tanx)2_

Explanation

Given:

The function is y=x2−tanx.

Formula used:

Quotient rule:

If f(x) and g(x) are differentiable functions, then the quotient rule is,

ddx[f(x)g(x)]=g(x)ddx[f(x)]−f(x)ddx[g(x)][g(x)]2 (1)

Calculation:

Apply the quotient rule as shown in equation (1).

Substitute x for f(x) and 2−tanx for g(x) in equation (1).

ddx[x2−tanx]=[2−tanx]ddx[x]−xddx[2−tanx][2−tanx]2 =(2−tanx)(1)−x(0−sec2x)(2−tanx)2=(2−tanx)−x(−sec2x)(2−tanx)2=2−tanx+xsec2x(2−tanx)2

Therefore, the differentiation of y=x2−tanx is 2−tanx+xsec2x    [2−tanx]2_.